An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

Kaushik, Harshal D.; Samadi, Sepideh; Yousefian, Farzad

doi:10.1109/TAC.2023.3251851

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

Journal Article · Thu Mar 02 00:00:00 EST 2023 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/TAC.2023.3251851· OSTI ID:3009630

^[1]; ^[2]; ^[2]

Bayer U.S. LLC, St. Louis, MO (United States)
Rutgers Univ., New Brunswick, NJ (United States)

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

View Accepted Manuscript (DOE)

Research Organization:: Rutgers Univ., Piscataway, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0023303

OSTI ID:: 3009630

Journal Information:: IEEE Transactions on Automatic Control, Journal Name: IEEE Transactions on Automatic Control Journal Issue: 12 Vol. 68; ISSN 0018-9286; ISSN 2334-3303; ISSN 1558-2523

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

References (14)

Robust solution of monotone stochastic linear complementarity problems Chen, Xiaojun; Zhang, Chao; Fukushima, Masao Mathematical Programming, Vol. 117, Issue 1-2 https://doi.org/10.1007/s10107-007-0163-z	journal	July 2007
Incremental constraint projection methods for variational inequalities Wang, Mengdi; Bertsekas, Dimitri P. Mathematical Programming, Vol. 150, Issue 2 https://doi.org/10.1007/s10107-014-0769-x	journal	May 2014
On smoothing, regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems Yousefian, Farzad; Nedić, Angelia; Shanbhag, Uday V. Mathematical Programming, Vol. 165, Issue 1 https://doi.org/10.1007/s10107-017-1175-y	journal	July 2017
Distributed nonconvex constrained optimization over time-varying digraphs Scutari, Gesualdo; Sun, Ying Mathematical Programming, Vol. 176, Issue 1-2 https://doi.org/10.1007/s10107-018-01357-w	journal	February 2019
Algorithmic Game Theory Nisan, Noam; Roughgarden, Tim; Tardos, Eva Cambridge University Press https://doi.org/10.1017/CBO9780511800481	book	September 2007
Distributed Constrained Optimization by Consensus-Based Primal-Dual Perturbation Method Chang, Tsung-Hui; Nedic, Angelia; Scaglione, Anna IEEE Transactions on Automatic Control, Vol. 59, Issue 6 https://doi.org/10.1109/TAC.2014.2308612	journal	June 2014
A Convergent Incremental Gradient Method with a Constant Step Size Blatt, Doron; Hero, Alfred O.; Gauchman, Hillel SIAM Journal on Optimization, Vol. 18, Issue 1 https://doi.org/10.1137/040615961	journal	January 2007
On the Convergence Rate of Incremental Aggregated Gradient Algorithms Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. A. SIAM Journal on Optimization, Vol. 27, Issue 2 https://doi.org/10.1137/15M1049695	journal	January 2017
Convergence Rate of Incremental Gradient and Incremental Newton Methods Gürbüzbalaban, M.; Ozdaglar, A.; Parrilo, P. A. SIAM Journal on Optimization, Vol. 29, Issue 4 https://doi.org/10.1137/17M1147846	journal	January 2019
A Method with Convergence Rates for Optimization Problems with Variational Inequality Constraints Kaushik, Harshal D.; Yousefian, Farzad SIAM Journal on Optimization, Vol. 31, Issue 3 https://doi.org/10.1137/20M1357378	journal	January 2021
Engineering and Economic Applications of Complementarity Problems Ferris, M. C.; Pang, J. S. SIAM Review, Vol. 39, Issue 4 https://doi.org/10.1137/S0036144595285963	journal	January 1997
Incremental Subgradient Methods for Nondifferentiable Optimization Nedic, Angelia; Bertsekas, Dimitri P. SIAM Journal on Optimization, Vol. 12, Issue 1 https://doi.org/10.1137/S1052623499362111	journal	January 2001
Solving Variational Inequalities with Stochastic Mirror-Prox Algorithm Juditsky, Anatoli; Nemirovski, Arkadi; Tauvel, Claire Stochastic Systems, Vol. 1, Issue 1 https://doi.org/10.1287/10-SSY011	journal	June 2011
Bilevel Distributed Optimization in Directed Networks Yousefian, Farzad 2021 American Control Conference (ACC) https://doi.org/10.23919/ACC50511.2021.9483429	conference	May 2021

Similar Records

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

Journal Article · Mon Feb 17 19:00:00 EST 2025 · SIAM Journal on Optimization · OSTI ID:3009725

An infeasible-start framework for convex quadratic optimization, with application to constraint-reduced interior-point and other methods

Journal Article · Tue Jul 20 20:00:00 EDT 2021 · Mathematical Programming · OSTI ID:1909160

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

Journal Article · Fri Dec 14 23:00:00 EST 2007 · Applied Mathematics and Optimization · OSTI ID:21064181

Related Subjects

convergence
linear programming

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

Citation Formats

References (14)

Similar Records

Related Subjects