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An Adaptive Refinement Algorithm for Discretizations of Nonconvex QCQP

Akshay Gupte, Arie M. C. A. Koster, Sascha Kuhnke, Christian Schulz, Bora Uçar
2022
We present an iterative algorithm to compute feasible solutions in reasonable running time to quadratically constrained quadratic programs (QCQPs), which form a challenging class of nonconvex continuous  ...  Since the quality of this solution heavily depends on the chosen discretization of the MILP, we iteratively adapt the discretization values based on the MILP solution of the previous iteration.  ...  Conclusion We presented an iterative algorithm that adaptively refines a MILP restriction of a QCQP.  ... 
doi:10.4230/lipics.sea.2022.24 fatcat:iqwfqw7rsrhhlctytxw7hynwpi

Introducing the quadratically-constrained quadratic programming framework in HPIPM [article]

Gianluca Frison, Jonathan Frey, Florian Messerer, Andrea Zanelli, Moritz Diehl
2021 arXiv   pre-print
The newly introduced QCQP framework provides full features parity with the original QP framework: three types of QCQPs (dense, optimal control and tree-structured optimal control QCQPs) and interior point  ...  Leveraging the modular structure of HPIPM, the new QCQP framework builds on the QP building blocks and similarly provides fast and reliable IPM solvers.  ...  softed state quadratic constraint The solution times for the QCQPs are within roughly a factor 2 of the solution time for the QP for all algorithmic combinations.  ... 
arXiv:2112.11872v1 fatcat:ozg637ry7ba2vhxaab4killgve

Model Predictive Control for On-Board-Optimized Attitude Guidance for Cometary Fly-By - Problem Statement, Solutions and V&V Process

Pedro Lourenço, João Franco, Tiago Milhano, João Branco
2021 Zenodo  
However, the unique challenges of on-board applications raise the need for a thorough analysis of the computational efficiency, reliability, accuracy, and robustness of the solution process.  ...  The problem is approximated in two ways: 1) A convex quadratically constrained quadratic program (QCQP) form, to be solved numerically by means of a QCQP solver. 2) A convex quadratic program (QP) form  ...  Furthermore, in case of failure of an actuator, input constraints can be appropriately adapted, to modify the control strategy accordingly.  ... 
doi:10.5281/zenodo.6411680 fatcat:yt3nmej5gjex5nzqrorzjj7d44

Radar Waveform Design for Extended Target Recognition under Detection Constraints

Huadong Meng, Yimin Wei, Xuhua Gong, Yimin Liu, Xiqin Wang
2012 Mathematical Problems in Engineering  
We formulate the code design in terms of a nonconvex, NP-hard quadratic optimization problem in the cases of both continuous and discrete phases.  ...  We address the problem of radar phase-coded waveform design for extended target recognition in the presence of colored Gaussian disturbance.  ...  The SDR technique can be applied to many nonconvex quadratically constrained quadratic programs QCQPs in an almost mechanical fashion 16 .  ... 
doi:10.1155/2012/289819 fatcat:gummo4gjoravxdk6yssuypwmgi

Pooling problems under perfect and imperfect competition [article]

Dimitri J. Papageorgiou, Stuart M. Harwood, Francisco Trespalacios
2021 arXiv   pre-print
We demonstrate that our provably optimal decomposition algorithm can handle some of the largest bilevel optimization problems with nonconvex lower-level problems ever considered in the literature.  ...  We present several bilevel formulations and numerical results of a novel decomposition algorithm.  ...  For this work, we adapt the approach of Harwood et al. [18] , which introduces an exact method for equilibrium problems with nonconvex structures.  ... 
arXiv:2110.03018v1 fatcat:bdrpsaonkzajfjwgoha46ljrb4

FIR Filter Design by Convex Optimization Using Directed Iterative Rank Refinement Algorithm

Mehmet Dedeoglu, Yasar Kemal Alp, Orhan Arikan
2016 IEEE Transactions on Signal Processing  
To obtain a rank-1 solution, we propose a novel Directed Iterative Rank Refinement (DIRR) algorithm, where at each iteration a matrix is obtained by solving a convex optimization problem.  ...  By using lifting techniques, the design of a length-FIR filter can be formulated as a convex semidefinite program (SDP) in terms of an matrix that must be rank-1.  ...  This framework is extended to linear phase FIR filter design by using discrete cosine transform (DCT) instead of discrete Fourier transform (DFT) in [12] .  ... 
doi:10.1109/tsp.2016.2515062 fatcat:j2ehjvzgxzh4bo5o6yquhpapym

Advanced optimization methods for power systems

P. Panciatici, M.C. Campi, S. Garatti, S.H. Low, D.K. Molzahn, A.X. Sun, L. Wehenkel
2014 2014 Power Systems Computation Conference  
, as well as novel machine learning and randomized algorithms, are highlighted.  ...  The practical relevance of these developments for power systems planning and operation are discussed, and the opportunities for combining them, together with high-performance computing and big data infrastructures  ...  ACKNOWLEDGMENTS The authors acknowledge the support of their funding organisms of the present work; the scientific responsibility of the statements of this paper remain with the authors.  ... 
doi:10.1109/pscc.2014.7038504 dblp:conf/pscc/PanciaticiCGLMS14 fatcat:w6lh2n4cpvhl5fbcomdmnwvwye

Relaxations and discretizations for the pooling problem

Akshay Gupte, Shabbir Ahmed, Santanu S. Dey, Myun Seok Cheon
2016 Journal of Global Optimization  
Valid inequalities are derived for the discretized models, which are formulated as mixed integer linear programs.  ...  Finally, we propose discretization methods for inner approximating the feasible region and obtaining good upper bounds.  ...  This gives us an estimate of how well discretization methods might perform if implemented as a heuristic in a branch-and-cut algorithm.  ... 
doi:10.1007/s10898-016-0434-4 fatcat:x4svzvfpbbg2lbyf6m6h6lxpwe

Model Predictive Control of Internal Combustion Engines: A Review and Future Directions

Armin Norouzi, Hamed Heidarifar, Mahdi Shahbakhti, Charles Koch, Hoseinali Borhan
2021 Energies  
Methods of model predictive control (MPC) have shown promising results for real-time multi-objective optimal control of constrained multi-variable nonlinear systems, including ICEs.  ...  This paper reviews the application of MPC for ICEs and analyzes the recent developments in MPC that can be utilized in ECMs.  ...  Farrell for their insightful technical discussions during this study.  ... 
doi:10.3390/en14196251 fatcat:qhkjp37py5fjbdpoh47zraws7u

Non-convex mixed-integer nonlinear programming: A survey

Samuel Burer, Adam N. Letchford
2012 Surveys in Operations Research and Management Science  
For the case in which the objective and constraint functions are convex, some quite effective exact and heuristic algorithms are available.  ...  A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs).  ...  Misener & Floudas [106] present an exact algorithm for non-convex mixed 0-1 QCQPs that is based on branch-and-reduce, together with cutting planes derived from the consideration of polyhedra involving  ... 
doi:10.1016/j.sorms.2012.08.001 fatcat:ykgvnv2a6jd57lrhjh4qtxd4pi

Solving Almost all Systems of Random Quadratic Equations [article]

Gang Wang and Georgios B. Giannakis and Yousef Saad and Jie Chen
2017 arXiv   pre-print
This paper deals with finding an n-dimensional solution x to a system of quadratic equations of the form y_i=|〈a_i,x〉|^2 for 1< i < m, which is also known as phase retrieval and is NP-hard in general.  ...  , followed by successive refinements based upon a sequence of iteratively reweighted (generalized) gradient iterations.  ...  Implementing K = 4 masks, each algorithm performs independently over each band 100 power iterations for an initial guess, which was refined by 100 gradient iterations.  ... 
arXiv:1705.10407v1 fatcat:khpmh6kwfrezlmv7itz2m5mye4

Proximity Queries Between Convex Objects: An Interior Point Approach for Implicit Surfaces

Nilanjan Chakraborty, Jufeng Peng, Srinivas Akella, John E. Mitchell
2008 IEEE Transactions on robotics  
This paper presents an interior point approach to exact distance computation between convex objects represented as intersections of implicit surfaces.  ...  We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved.  ...  Thanks to Richard Waltz for help with KNITRO, Buck Clay for graphics software, and Jeff Trinkle, Steve Berard, Binh Nguyen, and Frank Luk for useful discussions.  ... 
doi:10.1109/tro.2007.914851 fatcat:ilcb2frqzfau7mdqbspk744mze

Tutorials on Advanced Optimization Methods [article]

Wei Wei
2020 arXiv   pre-print
It is one of the main references for an optimization course taught at Tsinghua University.  ...  Fundamental algorithms are not the main focus. This material is a good reference for self-learners who have basic knowledge in linear algebra and linear programming.  ...  The procedure of the adaptive scenario generation algorithm for ARO is summarized in Algorithm C.2.  ... 
arXiv:2007.13545v1 fatcat:o5rx62tjzvfunitksen4dlci6m

Ping-pong beam training for reciprocal channels with delay spread

Elisabeth de Carvalho, Jorgen Bach Andersen
2015 2015 49th Asilomar Conference on Signals, Systems and Computers  
We call the method Successive QCQP Refinement (SQR). We evaluate SQR performance and show that it outperforms existing methods without a significant computational burden.  ...  A distributed consensus algorithm for estimating the number of nodes in a wireless sensor network in the presence of communication noise is proposed.  ...  In this paper, an adaptive greedy matching pursuit algorithm is proposed for estimating sparse target scenes.  ... 
doi:10.1109/acssc.2015.7421451 dblp:conf/acssc/CarvalhoA15 fatcat:mqokuvnh3zg45licnfbgxyvxfu

Implementation of Fog computing for reliable E-health applications

Razvan Craciunescu, Albena Mihovska, Mihail Mihaylov, Sofoklis Kyriazakos, Ramjee Prasad, Simona Halunga
2015 2015 49th Asilomar Conference on Signals, Systems and Computers  
Finally, we will provide 'structured' CS algorithms for the joint estimation scheme and evaluate its performance.  ...  An important aspect is robust and resource efficient preamble design to minimize missed detection and false alarm probabilities of service requests.  ...  In this paper, an adaptive greedy matching pursuit algorithm is proposed for estimating sparse target scenes.  ... 
doi:10.1109/acssc.2015.7421170 dblp:conf/acssc/CraciunescuMMKP15 fatcat:qm6mki5z6bcvrfimkmqjyrxaxm
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