Nonconvex robust programming via value-function optimization

Ying Cui (), Ziyu He () and Jong-Shi Pang ()
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Ying Cui: University of Minnesota
Ziyu He: University of Southern California
Jong-Shi Pang: University of Southern California

Computational Optimization and Applications, 2021, vol. 78, issue 2, No 4, 450 pages

Abstract: Abstract Convex programming based robust optimization is an active research topic in the past two decades, partially because of its computational tractability for many classes of optimization problems and uncertainty sets. However, many problems arising from modern operations research and statistical learning applications are nonconvex even in the nominal case, let alone their robust counterpart. In this paper, we introduce a systematic approach for tackling the nonconvexity of the robust optimization problems that is usually coupled with the nonsmoothness of the objective function brought by the worst-case value function. A majorization-minimization algorithm is presented to solve the penalized min-max formulation of the robustified problem that deterministically generates a “better” solution compared with the starting point (that is usually chosen as an unrobustfied optimal solution). A generalized saddle-point theorem regarding the directional stationarity is established and a game-theoretic interpretation of the computed solutions is provided. Numerical experiments show that the computed solutions of the nonconvex robust optimization problems are less sensitive to the data perturbation compared with the unrobustfied ones.

Keywords: Robust optimization; Nonconvex; Nonsmooth; Value function (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10589-020-00245-4

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