Robust approximation of chance constrained optimization with polynomial perturbation

Bo Rao (), Liu Yang (), Suhan Zhong () and Guangming Zhou ()
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Bo Rao: Xiangtan University
Liu Yang: Xiangtan University
Suhan Zhong: Texas A&M University
Guangming Zhou: Xiangtan University

Computational Optimization and Applications, 2024, vol. 89, issue 3, No 12, 977-1003

Abstract: Abstract This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a robust approximation by replacing the chance constraint with a robust constraint over an uncertainty set. When the objective function is linear or SOS-convex, the robust approximation can be equivalently transformed into linear conic optimization. Semidefinite relaxation algorithms are proposed to solve these linear conic transformations globally and their convergent properties are studied. We also introduce a heuristic method to find efficient uncertainty sets such that optimizers of the robust approximation are feasible to the original problem. Numerical experiments are given to show the efficiency of our method.

Keywords: Chance constrained optimization; Robust optimization; Nonnegative polynomial; Semidefinite relaxation; 90C15; 90C17; 90C22; 90C59 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-024-00602-7

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