IA Scholar Query: Further Development of a Primal-Dual Interior Point Method.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 30 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440A steady diet of images. The European migrant crisis, border policy and political aesthetics
https://scholar.archive.org/work/lmjtfax4d5hdtor7rzyespoc6m
This thesis sits at the ever-expanding margins of borders studies, focusing on the cultural and aesthetic significance of border constructions and regimes. Whilst building upon a base of key modern geopolitical literature, it engages with a reflection on whether the ongoing European Crisis is one of migrants, of borders, or of European identity itself. Events since 2015,and the European Union's (EU)flawed response, challenge its vision of being a normative power in global politics. Through a lack of Union solidarity and ongoing evidence of hypocrisy, it is clear that the (re)fencing of Europe has become a Rorschach test for the continent as much as it has for the individual member states. From this flows a discussion around counter-hegemonic method, employing the concepts of political aesthetics, especially through visual regimes of news media and photojournalism. If political writings traditionally deal with the state and aesthetical writings with art and drama, the blending of the two enable to present new perspectives of the concept of Europe's crisis. The necroaesthetics discussed deal with both the bodies of migrants, and the teichopolitical spaces of camps and (re)fenced borders. By concentrating on the violence of borders as racialised contact zones in their multiple and expanding manifestations , this approach helps to challenge and critique governmental narratives related to migration and its perceived threat to the political class. This can be seen through the European memento mori of a century of camps and barbed wire which provoke the hallucinatory presence of previous war images, and border barriers of the last century.Richard A. Vogtwork_lmjtfax4d5hdtor7rzyespoc6mWed, 30 Nov 2022 00:00:00 GMTDistributed Online Optimization for Multi-Agent Optimal Transport
https://scholar.archive.org/work/j4bzoqtyvjgirjmzoyq3t6lrny
We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-agent systems. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of transport, with the additional constraint of distributed implementation. Using optimal transport theory, we realize the solution as an iterative transport based on a proximal descent scheme. At each stage of the transport, the agents implement an online, distributed primal-dual algorithm to obtain local estimates of the Kantorovich potential for optimal transport from the current distribution of the collective to the target distribution. Using these estimates as their local objective functions, the agents then implement the transport by proximal descent. This two-step process is carried out recursively by the agents to converge asymptotically to the target distribution. We rigorously establish the underlying theoretical framework for the algorithm and test its behavior via numerical experiments.Vishaal Krishnan, Sonia Martínezwork_j4bzoqtyvjgirjmzoyq3t6lrnyWed, 30 Nov 2022 00:00:00 GMTQuasi-stable Coloring for Graph Compression: Approximating Max-Flow, Linear Programs, and Centrality
https://scholar.archive.org/work/yjz42a5poraqxfje7zxwwyjtaa
We propose quasi-stable coloring, an approximate version of stable coloring. Stable coloring, also called color refinement, is a well-studied technique in graph theory for classifying vertices, which can be used to build compact, lossless representations of graphs. However, its usefulness is limited due to its reliance on strict symmetries. Real data compresses very poorly using color refinement. We propose the first, to our knowledge, approximate color refinement scheme, which we call quasi-stable coloring. By using approximation, we alleviate the need for strict symmetry, and allow for a tradeoff between the degree of compression and the accuracy of the representation. We study three applications: Linear Programming, Max-Flow, and Betweenness Centrality, and provide theoretical evidence in each case that a quasi-stable coloring can lead to good approximations on the reduced graph. Next, we consider how to compute a maximal quasi-stable coloring: we prove that, in general, this problem is NP-hard, and propose a simple, yet effective algorithm based on heuristics. Finally, we evaluate experimentally the quasi-stable coloring technique on several real graphs and applications, comparing with prior approximation techniques. A reference implementation and the experiment code are available at https://github.com/mkyl/QuasiStableColors.jl .Moe Kayali, Dan Suciuwork_yjz42a5poraqxfje7zxwwyjtaaTue, 29 Nov 2022 00:00:00 GMTLCQPow – A Solver for Linear Complementarity Quadratic Programs
https://scholar.archive.org/work/kq5k42pc2nhgpa6sbsih2vgdum
In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in engineering and economics, and they are challenging to solve due to their structural violation of standard constraint qualifications, and highly nonconvex, nonsmooth feasible sets. This work extends a previously presented algorithm based on a sequential convex programming approach applied to a standard penalty reformulation. We examine the behavior of local convergence and introduce new algorithmic features. Competitive performance profiles are presented in comparison to state-of-the-art solvers and solution variants in both existing and new benchmarks.Jonas Hall, Armin Nurkanovic, Florian Messerer, Moritz Diehlwork_kq5k42pc2nhgpa6sbsih2vgdumTue, 29 Nov 2022 00:00:00 GMTFETI-DP preconditioners for 2D Biot model with discontinuous Galerkin discretization
https://scholar.archive.org/work/pq6ou2ryebfl7ncza6dlooqbea
Dual-primal FETI (FETI-DP) preconditioners are developed for a 2D Biot model. The model is formulated with mixed-finite elements as a saddle-point problem. The displacement 𝐮 and the Darcy flux flow 𝐳 are represented with P_1 piecewise continuous elements and pore-pressure p with P_0 piecewise constant elements, i.e., overall three fields with a stabilizing term. We have tested the functionality of FETI-DP with and without Dirichlet preconditioners. Numerical experiments show a signature of scalability of the resulting parallel algorithm in the compressible elasticity with permeable Darcy flow as well as almost incompressible elasticity.Pilhwa Leework_pq6ou2ryebfl7ncza6dlooqbeaMon, 28 Nov 2022 00:00:00 GMTControlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraints
https://scholar.archive.org/work/xwysh4s4afdnbbczgh4snwidd4
The performance of trained neural networks is robust to harsh levels of pruning. Coupled with the ever-growing size of deep learning models, this observation has motivated extensive research on learning sparse models. In this work, we focus on the task of controlling the level of sparsity when performing sparse learning. Existing methods based on sparsity-inducing penalties involve expensive trial-and-error tuning of the penalty factor, thus lacking direct control of the resulting model sparsity. In response, we adopt a constrained formulation: using the gate mechanism proposed by Louizos et al. (2018), we formulate a constrained optimization problem where sparsification is guided by the training objective and the desired sparsity target in an end-to-end fashion. Experiments on CIFAR-10, 100, TinyImageNet, and ImageNet using WideResNet and ResNet18, 50 models validate the effectiveness of our proposal and demonstrate that we can reliably achieve pre-determined sparsity targets without compromising on predictive performance.Jose Gallego-Posada and Juan Ramirez and Akram Erraqabi and Yoshua Bengio and Simon Lacoste-Julienwork_xwysh4s4afdnbbczgh4snwidd4Sun, 27 Nov 2022 00:00:00 GMTSpeeding-up Symbol-Level Precoding Using Separable and Dual Optimizations
https://scholar.archive.org/work/vfocjkx6jbf4tj7mtookrfgapm
Symbol-level precoding (SLP) manipulates the transmitted signals to accurately exploit the multi-user interference (MUI) in the multi-user downlink. This enables that all the resultant interference contributes to correct detection, which is the so-called constructive interference (CI). Its performance superiority comes at the cost of solving a nonlinear optimization problem on a symbol-by-symbol basis, for which the resulting complexity becomes prohibitive in realistic wireless communication systems. In this paper, we investigate low-complexity SLP algorithms for both phase-shift keying (PSK) and quadrature amplitude modulation (QAM). Specifically, we first prove that the max-min SINR balancing (SB) SLP problem for PSK signaling is not separable, which is contrary to the power minimization (PM) SLP problem, and accordingly, existing decomposition methods are not applicable. Next, we establish an explicit duality between the PM-SLP and SB-SLP problems for PSK modulation. The proposed duality facilitates obtaining the solution to the SB-SLP given the solution to the PM-SLP without the need for one-dimension search, and vice versa. We then propose a closed-form power scaling algorithm to solve the SB-SLP via PM-SLP to take advantage of the separability of the PM-SLP. As for QAM modulation, we convert the PM-SLP problem into a separable equivalent optimization problem, and decompose the new problem into several simple parallel subproblems with closed-form solutions, leveraging the proximal Jacobian alternating direction method of multipliers (PJ-ADMM). We further prove that the proposed duality can be generalized to the multi-level modulation case, based on which a power scaling parallel inverse-free algorithm is also proposed to solve the SB-SLP for QAM signaling. Numerical results show that the proposed algorithms offer optimal performance with lower complexity than the state-of-the-art.Junwen Yang, Ang Li, Xuewen Liao, Christos Masouroswork_vfocjkx6jbf4tj7mtookrfgapmSun, 27 Nov 2022 00:00:00 GMTAn Efficient HPR Algorithm for the Wasserstein Barycenter Problem with O(Dim(P)/ε) Computational Complexity
https://scholar.archive.org/work/rxub74mefbfi7bsfnnsub45u4m
In this paper, we propose and analyze an efficient Halpern-Peaceman-Rachford (HPR) algorithm for solving the Wasserstein barycenter problem (WBP) with fixed supports. While the Peaceman-Rachford (PR) splitting method itself may not be convergent for solving the WBP, the HPR algorithm can achieve an O(1/ε) non-ergodic iteration complexity with respect to the Karush-Kuhn-Tucker (KKT) residual. More interestingly, we propose an efficient procedure with linear time computational complexity to solve the linear systems involved in the subproblems of the HPR algorithm. As a consequence, the HPR algorithm enjoys an O( Dim(P)/ε) non-ergodic computational complexity in terms of flops for obtaining an ε-optimal solution measured by the KKT residual for the WBP, where Dim(P) is the dimension of the variable of the WBP. This is better than the best-known complexity bound for the WBP. Moreover, the extensive numerical results on both the synthetic and real data sets demonstrate the superior performance of the HPR algorithm for solving the large-scale WBP.Guojun Zhang, Yancheng Yuan, Defeng Sunwork_rxub74mefbfi7bsfnnsub45u4mSun, 27 Nov 2022 00:00:00 GMTInformation Geometry of Dynamics on Graphs and Hypergraphs
https://scholar.archive.org/work/zzobax2mnngiljvk6zetumgap4
We introduce a new information-geometric structure of dynamics on discrete objects such as graphs and hypergraphs. The setup consists of two dually flat structures built on the vertex and edge spaces, respectively. The former is the conventional duality between density and potential, e.g., the probability density and its logarithmic form induced by a convex thermodynamic function. The latter is the duality between flux and force induced by a convex and symmetric dissipation function, which drives the dynamics on the manifold. These two are connected topologically by the homological algebraic relation induced by the underlying discrete objects. The generalized gradient flow in this doubly dual flat structure is an extension of the gradient flows on Riemannian manifolds, which include Markov jump processes and nonlinear chemical reaction dynamics as well as the natural gradient and mirror descent. The information-geometric projections on this doubly dual flat structure lead to the information-geometric generalizations of Helmholtz-Hodge-Kodaira decomposition and Otto structure in L^2 Wasserstein geometry. The structure can be extended to non-gradient nonequilibrium flow, from which we also obtain the induced dually flat structure on cycle spaces. This abstract but general framework can extend the applicability of information geometry to various problems of linear and nonlinear dynamics.Tetsuya J. Kobayashi, Dimitri Loutchko, Atsushi Kamimura, Shuhei Horiguchi, Yuki Sughiyamawork_zzobax2mnngiljvk6zetumgap4Sat, 26 Nov 2022 00:00:00 GMTFast Algorithms for Packing Proportional Fairness and its Dual
https://scholar.archive.org/work/wbpcd4d6urf35gm4vkwip7lmru
The proportional fair resource allocation problem is a major problem studied in flow control of networks, operations research, and economic theory, where it has found numerous applications. This problem, defined as the constrained maximization of ∑_i log x_i, is known as the packing proportional fairness problem when the feasible set is defined by positive linear constraints and x ∈ℝ^n_≥ 0. In this work, we present a distributed accelerated first-order method for this problem which improves upon previous approaches. We also design an algorithm for the optimization of its dual problem. Both algorithms are width-independent. Finally, we show the latter problem has applications to the volume reduction of bounding simplices in an old linear programming algorithm of (YL82), and we obtain some improvements as a result.Francisco Criado, David Martínez-Rubio, Sebastian Pokuttawork_wbpcd4d6urf35gm4vkwip7lmruSat, 26 Nov 2022 00:00:00 GMTMinimax Problems with Coupled Linear Constraints: Computational Complexity, Duality and Solution Methods
https://scholar.archive.org/work/pu3pumm33nhqlc2aywt5q6aonm
In this work we study a special minimax problem where there are linear constraints that couple both the minimization and maximization decision variables. The problem is a generalization of the traditional saddle point problem (which does not have the coupling constraint), and it finds applications in wireless communication, game theory, transportation, just to name a few. We show that the considered problem is challenging, in the sense that it violates the classical max-min inequality, and that it is NP-hard even under very strong assumptions (e.g., when the objective is strongly convex-strongly concave). We then develop a duality theory for it, and analyze conditions under which the duality gap becomes zero. Finally, we study a class of stationary solutions defined based on the dual problem, and evaluate their practical performance in an application on adversarial attacks on network flow problems.Ioannis Tsaknakis, Mingyi Hong, Shuzhong Zhangwork_pu3pumm33nhqlc2aywt5q6aonmSat, 26 Nov 2022 00:00:00 GMTThe Generalized Elastic Net for least squares regression with network-aligned signal and correlated design
https://scholar.archive.org/work/od5fmwmjj5goroznqeiayj66ku
We propose a novel ℓ_1+ℓ_2-penalty, which we refer to as the Generalized Elastic Net, for regression problems where the feature vectors are indexed by vertices of a given graph and the true signal is believed to be smooth or piecewise constant with respect to this graph. Under the assumption of correlated Gaussian design, we derive upper bounds for the prediction and estimation errors, which are graph-dependent and consist of a parametric rate for the unpenalized portion of the regression vector and another term that depends on our network alignment assumption. We also provide a coordinate descent procedure based on the Lagrange dual objective to compute this estimator for large-scale problems. Finally, we compare our proposed estimator to existing regularized estimators on a number of real and synthetic datasets and discuss its potential limitations.Huy Tran, Sansen Wei, Claire Donnatwork_od5fmwmjj5goroznqeiayj66kuFri, 25 Nov 2022 00:00:00 GMTConditional Gradient Methods
https://scholar.archive.org/work/b2imrksvmfclhaik7ghfh6bcte
The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are especially useful in convex optimization when linear optimization is cheaper than projections. The selection of the material has been guided by the principle of highlighting crucial ideas as well as presenting new approaches that we believe might become important in the future, with ample citations even of old works imperative in the development of newer methods. Yet, our selection is sometimes biased, and need not reflect consensus of the research community, and we have certainly missed recent important contributions. After all the research area of Frank--Wolfe is very active, making it a moving target. We apologize sincerely in advance for any such distortions and we fully acknowledge: We stand on the shoulder of giants.Gábor Braun, Alejandro Carderera, Cyrille W. Combettes, Hamed Hassani, Amin Karbasi, Aryan Mokhtari, Sebastian Pokuttawork_b2imrksvmfclhaik7ghfh6bcteFri, 25 Nov 2022 00:00:00 GMTA dichotomy theory for height functions
https://scholar.archive.org/work/je55i7cxxzb43ar7oh4hsaktmu
Height functions are random functions on a given graph, in our case integer-valued functions on the two-dimensional square lattice. We consider gradient potentials which (informally) lie between the discrete Gaussian and solid-on-solid model (inclusive). The phase transition in this model, known as the roughening transition, Berezinskii-Kosterlitz-Thouless transition, or localisation-delocalisation transition, was established rigorously in the 1981 breakthrough work of Fröhlich and Spencer. It was not until 2005 that Sheffield derived continuity of the phase transition. First, we establish sharpness, in the sense that covariances decay exponentially in the localised phase. Second, we show that the model is delocalised at criticality, in the sense that the set of potentials inducing localisation is open in a natural topology. Third, we prove that the pointwise variance of the height function is at least clog n in the delocalised regime, where n is the distance to the boundary, and where c>0 denotes a universal constant. This implies that the effective temperature of any potential cannot lie in the interval (0,c) (whenever it is well-defined), and jumps from 0 to at least c at the critical point. We call this range of forbidden values the effective temperature gap.Piet Lammerswork_je55i7cxxzb43ar7oh4hsaktmuFri, 25 Nov 2022 00:00:00 GMTTailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications
https://scholar.archive.org/work/hr5zalzew5durek3lufp5c45zu
Mixed-integer model predictive control (MI-MPC) can be a powerful tool for modeling hybrid control systems. In case of a linear-quadratic objective in combination with linear or piecewise-linear system dynamics and inequality constraints, MI-MPC needs to solve a mixed-integer quadratic program (MIQP) at each sampling time step. This paper presents a collection of block-sparse presolve techniques to efficiently remove decision variables, and to remove or tighten inequality constraints, tailored to mixed-integer optimal control problems (MIOCP). In addition, we describe a novel heuristic approach based on an iterative presolve algorithm to compute a feasible but possibly suboptimal MIQP solution. We present benchmarking results for a C code implementation of the proposed BB-ASIPM solver, including a branch-and-bound (B&B) method with the proposed tailored presolve techniques and an active-set based interior point method (ASIPM), compared against multiple state-of-the-art MIQP solvers on a case study of motion planning with obstacle avoidance constraints. Finally, we demonstrate the computational performance of the BB-ASIPM solver on the dSPACE Scalexio real-time embedded hardware using a second case study of stabilization for an underactuated cart-pole with soft contacts.Rien Quirynen, Stefano Di Cairanowork_hr5zalzew5durek3lufp5c45zuWed, 23 Nov 2022 00:00:00 GMTBnB-DAQP: A Mixed-Integer QP Solver for Embedded Applications
https://scholar.archive.org/work/ilvbfwbjmfeptdjm27bapqcozq
We propose a mixed-integer quadratic programming (QP) solver that is suitable for use in embedded applications, for example, hybrid model predictive control (MPC). The solver is based on the branch-and-bound method, and uses a recently proposed dual active-set solver for solving the resulting QP relaxations. Moreover, we tailor the search of the branch-and-bound tree to be suitable for embedded applications on limited hardware; we show, for example, how a node in the branch-and-bound tree can be represented by only two integers. The embeddability of the solver is shown by successfully running MPC of an inverted pendulum on a cart with contact forces on an MCU with limited memory and computing power.Daniel Arnström, Daniel Axehillwork_ilvbfwbjmfeptdjm27bapqcozqWed, 23 Nov 2022 00:00:00 GMTA Moment-Matching Approach to Testable Learning and a New Characterization of Rademacher Complexity
https://scholar.archive.org/work/l6wo4h7osfbutiekfn32vrzroq
A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of testable learning, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to require that the learner succeed whenever the unknown distribution passes the corresponding test. In this model, they gave an efficient algorithm for learning halfspaces under testable assumptions that are provably satisfied by Gaussians. In this paper we give a powerful new approach for developing algorithms for testable learning using tools from moment matching and metric distances in probability. We obtain efficient testable learners for any concept class that admits low-degree sandwiching polynomials, capturing most important examples for which we have ordinary agnostic learners. We recover the results of Rubinfeld and Vasilyan as a corollary of our techniques while achieving improved, near-optimal sample complexity bounds for a broad range of concept classes and distributions. Surprisingly, we show that the information-theoretic sample complexity of testable learning is tightly characterized by the Rademacher complexity of the concept class, one of the most well-studied measures in statistical learning theory. In particular, uniform convergence is necessary and sufficient for testable learning. This leads to a fundamental separation from (ordinary) distribution-specific agnostic learning, where uniform convergence is sufficient but not necessary.Aravind Gollakota, Adam R. Klivans, Pravesh K. Kothariwork_l6wo4h7osfbutiekfn32vrzroqWed, 23 Nov 2022 00:00:00 GMTEnd-to-end resource analysis for quantum interior point methods and portfolio optimization
https://scholar.archive.org/work/qqjpiwjbavd7dmso7ufco4m674
We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant pre-factors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage.Alexander M. Dalzell, B. David Clader, Grant Salton, Mario Berta, Cedric Yen-Yu Lin, David A. Bader, Nikitas Stamatopoulos, Martin J. A. Schuetz, Fernando G. S. L. Brandão, Helmut G. Katzgraber, William J. Zengwork_qqjpiwjbavd7dmso7ufco4m674Tue, 22 Nov 2022 00:00:00 GMTLearning context-aware adaptive solvers to accelerate quadratic programming
https://scholar.archive.org/work/zm5iyoocxrhkbhtgdqrspf6dgi
Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various types of QP, its convergence speed is known to be highly dependent on the step-size parameter ρ. Due to the absence of a general rule for setting ρ, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust ρ to accelerate ADMM. CA-ADMM extracts the spatio-temporal context, which captures the dependency of the primal and dual variables of QP and their temporal evolution during the ADMM iterations. CA-ADMM chooses ρ based on the extracted context. Through extensive numerical experiments, we validated that CA-ADMM effectively generalizes to unseen QP problems with different sizes and classes (i.e., having different QP parameter structures). Furthermore, we verified that CA-ADMM could dynamically adjust ρ considering the stage of the optimization process to accelerate the convergence speed further.Haewon Jung, Junyoung Park, Jinkyoo Parkwork_zm5iyoocxrhkbhtgdqrspf6dgiTue, 22 Nov 2022 00:00:00 GMTA Light-speed Linear Program Solver for Personalized Recommendation with Diversity Constraints
https://scholar.archive.org/work/o5n52hbx5bghtiih3vge6isogy
We study a structured linear program (LP) that emerges in the need of ranking candidates or items in personalized recommender systems. Since the candidate set is only known in real time, the LP also needs to be formed and solved in real time. Latency and user experience are major considerations, requiring the LP to be solved within just a few milliseconds. Although typical instances of the problem are not very large in size, this stringent time limit appears to be beyond the capability of most existing (commercial) LP solvers, which can take 20 milliseconds or more to find a solution. Thus, reliable methods that address the real-world complication of latency become necessary. In this paper, we propose a fast specialized LP solver for a structured problem with diversity constraints. Our method solves the dual problem, making use of the piece-wise affine structure of the dual objective function, with an additional screening technique that helps reduce the dimensionality of the problem as the algorithm progresses. Experiments reveal that our method can solve the problem within roughly 1 millisecond, yielding a 20x improvement in speed over efficient off-the-shelf LP solvers. This speed-up can help improve the quality of recommendations without affecting user experience, highlighting how optimization can provide solid orthogonal value to machine-learned recommender systems.Haoyue Wang, Miao Cheng, Kinjal Basu, Aman Gupta, Keerthi Selvaraj, Rahul Mazumderwork_o5n52hbx5bghtiih3vge6isogyTue, 22 Nov 2022 00:00:00 GMT