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Finite-Sum Coupled Compositional Stochastic Optimization: Theory and Applications [article]

Bokun Wang, Tianbao Yang
2022 arXiv   pre-print
We refer to this family of problems as finite-sum coupled compositional optimization (FCCO).  ...  This paper studies stochastic optimization for a sum of compositional functions, where the inner-level function of each summand is coupled with the corresponding summation index.  ...  Acknowledgements: We thank Yao Yao for spotting several mistakes in the proof and Gang Li for discussing the experiments on p-norm Push optimization.  ... 
arXiv:2202.12396v3 fatcat:m5bcbxpfzzb4pddz5k5asmnjsm

Special Issue: Optimization and Stochastic Control in Finance, Journal of Optimization Theory and Applications

Bruno Bouchard, H. Mete Soner, Nizar Touzi
2018 Journal of Optimization Theory and Applications  
theory.  ...  The authors formulate a finite-player linear-quadratic stochastic differential game with delay where the banks monitor the log-monetary reserves, the delay being due to the clearing of debt obligations  ...  Pasiliao incorporates the importance sampling technique into the stochastic alternating direction method of multipliers, with application to a class of stochastic composite problems with linear equality  ... 
doi:10.1007/s10957-018-1409-z fatcat:r3t35bcf6rap3mfqcpduyespra

Stochastic Forward–Backward Splitting for Monotone Inclusions

Lorenzo Rosasco, Silvia Villa, Bang Công Vũ
2016 Journal of Optimization Theory and Applications  
We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator.  ...  The algorithm we propose is a natural stochastic extension of the classical forward-backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as  ...  If in addition B is a gradient operator and G is finite dimensional, we are in the classical setting of stochastic optimization [24] .  ... 
doi:10.1007/s10957-016-0893-2 fatcat:ix6l5fv3xrhgvnlekp3v7toh7q

Grasshopper Optimization Algorithm: Theory, Variants, and Applications

Yassine Meraihi, Asma Benmessaoud Gabis, Seyedali Mirjalili, Amar Ramdane-Cherif
2021 IEEE Access  
It also discusses the main applications of GOA in various fields such as scheduling, economic dispatch, feature selection, load frequency control, distributed generation, wind energy system, and other  ...  Grasshopper Optimization Algorithm (GOA) is a recent swarm intelligence algorithm inspired by the foraging and swarming behavior of grasshoppers in nature.  ...  composite).  ... 
doi:10.1109/access.2021.3067597 fatcat:4deeotokfjb3dc2f4egf3qqymy

Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time

Asgar Jamneshan, Michael Kupper, José Miguel Zapata-García
2020 Journal of Optimization Theory and Applications  
We prove a general existence result in stochastic optimal control in discrete time, where controls, taking values in conditional metric spaces, depend on the current information and past decisions.  ...  The general form of the problem lies beyond the scope of standard techniques in stochastic control theory, the main novelty is a formalization in conditional metric space and the use of conditional analysis  ...  as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.  ... 
doi:10.1007/s10957-020-01711-z fatcat:k5gbvtc4cvg4xohr6qly5u6rpe

Convergence analysis of gradient descent stochastic algorithms

A. Shapiro, Y. Wardi
1996 Journal of Optimization Theory and Applications  
This paper proves convergence of a sample-path based stochastic gradient-descent algorithm for optimizing expected-value performance measures in discrete event systems.  ...  The algorithm uses increasing precision at successive iterations, and it moves against the direction of a generalized gradient of the computed sample performance function.  ...  for a stochastic, simulation-based algorithm for optimization of expected-value performance measures in discrete event systems.  ... 
doi:10.1007/bf02190104 fatcat:gndsm5ahgvbnbbedoaseoeg4ly

Variable Smoothing for Weakly Convex Composite Functions

Axel Böhm, Stephen J. Wright
2021 Journal of Optimization Theory and Applications  
AbstractWe study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator.  ...  Applications include image reconstruction problems with regularizers that introduce less bias than the standard convex regularizers.  ...  Supposing that the step size λ ∈ ]0, min{ρ −1 /2, L −1 ∇h }], we have for all k ≥ 1 that min 2≤ j≤k+1 Journal of Optimization Theory and Applications (2021) 188:628-649  ... 
doi:10.1007/s10957-020-01800-z pmid:33746291 pmcid:PMC7929970 fatcat:noffnrltlbda7pp3wjk34jkgs4

Algorithms for Optimal Control of Stochastic Switching Systems

J. Hinz, N. Yap
2016 Theory of Probability and its Applications  
Optimal control problems of switching type with linear state dynamics are ubiquitous in applications of stochastic optimization.  ...  ALGORITHMS FOR OPTIMAL CONTROL 581 [21], local polynomial regression [11] , and neural networks [5] have been established.  ...  These kinds of questions are often framed within the realm of Markov decision theory, which can be viewed as discrete-time optimal stochastic control.  ... 
doi:10.1137/s0040585x97t987910 fatcat:odoav62e5jghrgdit4xmuive3a

A Review of the Theory and Applications of Optimal Subband and Transform Coders

P.P. Vaidyanathan, Sony Akkarakaran
2001 Applied and Computational Harmonic Analysis  
Filter banks are used today not only for signal compression, but have found applications in signal denoising and in digital communications.  ...  The problem of optimizing digital filter banks based on input statistics was perhaps first addressed nearly four decades ago by Huang and Schultheiss.  ...  Since then the signal processing community has made many advances in the theory of filter banks, wavelets, and their applications.  ... 
doi:10.1006/acha.2000.0344 fatcat:4enx7hxy5nbihkfbwwy2drfwaa

On a Monotone Scheme for Nonconvex Nonsmooth Optimization with Applications to Fracture Mechanics

Daria Ghilli, Karl Kunisch
2019 Journal of Optimization Theory and Applications  
Its performance is also compared to two alternative algorithms for nonsmooth nonconvex optimization arising in optimal control and mathematical imaging.  ...  A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10957-019-01545-4 pmid:31975742 pmcid:PMC6944259 fatcat:bakybw3tdzg5zpdiyejjwkbp6m

Vector variational inequalities and related topics: A survey of theory and applications

2019 Applied Set-Valued Analysis and Optimization  
By giving several examples and presenting the necessary mathematical background and theories, the survey attempts to draw a broad audience and is accessible to students in mathematics and engineering.  ...  Finally, we give a brief analysis of stochastic vector variational inequalities, generalized problems and numerical methods.  ...  Franco Giannessi and Prof. Christiane Tammer for a careful reading and numerous helpful suggestions on an earlier draft of this manuscript, which helped to improve the paper significantly.  ... 
doi:10.23952/asvao.1.2019.3.04 fatcat:u2osdoat6nfwnnyncd2iev4yjy

On the Proximal Gradient Algorithm with Alternated Inertia

Franck Iutzeler, Jérôme Malick
2018 Journal of Optimization Theory and Applications  
The results are put into perspective by discussions on several extensions and illustrations on common regularized problems.  ...  Acknowledgements The work of the authors is partly supported by the PGMO Grant Advanced Non-smooth Optimization Methods for Stochastic Programming.  ...  Introduction In this paper, we consider the composite convex optimization problem min x∈R n F (x) := f (x) + g(x) (1) where the functions f and g are convex, and f is furthermore smooth.  ... 
doi:10.1007/s10957-018-1226-4 fatcat:xcm6p3nig5ektnfqfyptrws2p4

Alternative theoretical frameworks for finite horizon discrete-time stochastic optimal control

Steven E. Shreve, Dimitri P. Bertsekas
1977 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications  
A p-e-optimal policy is one which leads to a cost which differs from the optimal cost by less than e for p-almost every initial state. Even over a finite  ...  Witflin this framework all known results for finite horizon problems together with some new ones are proved and subsequently specialized.  ...  sense and the theory of_ DP is well developed (see e.g  ... 
doi:10.1109/cdc.1977.271560 fatcat:hnziluestjgbdmoemuobj4sq3q

An Ordinal Game Theory Approach to the Analysis and Selection of Partners in Public–Private Partnership Projects

Jamal Ouenniche, Aristotelis Boukouras, Mohammad Rajabi
2015 Journal of Optimization Theory and Applications  
To fill this gap, we model this decision problem as a static non-cooperative game of complete information and propose a new ordinal game theory algorithm for finding an optimal generalized Nash equilibrium  ...  The proposed ordinal game theory-based analysis framework can be used by the private sector to analyse any set of potential proposals most likely to be submitted by bidders and to assist with the choice  ...  Acceptable balance between Stakeholders' conflicting goals and objectives, e.g. third-party stakeholders such as international NGOs [54] Social (public) support and political support [57, 69] Favourable  ... 
doi:10.1007/s10957-015-0844-3 fatcat:teyxotjmjjem5ecif7dimkjliq

Barycentric Bounds in Stochastic Programming: Theory and Application [chapter]

Karl Frauendorfer, Daniel Kuhn, Michael Schürle
2010 International Series in Operations Research and Management Science  
To this end, we solve a stochastic optimization model for the management of non-maturing accounts and compare the bounds on maximum profit obtained with different partitioning strategies.  ...  The design and analysis of efficient approximation schemes is of fundamental importance in stochastic programming research.  ...  Evaluation of A l J,t and A u J,t requires calculation of a finite sum, while A t can usually be evaluated by means of numerical integration techniques.  ... 
doi:10.1007/978-1-4419-1642-6_5 fatcat:mjga36jpx5dvfahayedenyawza
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