Optimality Conditions and Duality in Nonsmooth Adjustable Robust Optimization Problems

Mai Van Duy (), Phan Quoc Khanh () and Nguyen Minh Tung ()
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Mai Van Duy: University of Science, Vietnam National University
Phan Quoc Khanh: Faculty of Mathematics and Statistics, Ton Duc Thang University
Nguyen Minh Tung: Ho Chi Minh University of Banking

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 3, No 16, 28 pages

Abstract: Abstract In this paper, we consider nonsmooth adjustable robust optimization problems and necessary/sufficient conditions based on qualification conditions and generalized convexity concepts. Verifiable sufficient conditions and useful relations for these qualification conditions are provided. Our analysis covers a wide range of uncertain sets commonly used in adjustable robust optimization, and we employ a dual approach to address non-reformulated cases of uncertain set, while also providing a direct approach to these problems through reformulation.

Keywords: Nonsmooth adjustable robust; Two-stage robust; Optimality condition; Constraint qualification; Generalized convexity; 90C34; 90C46; 90C32 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02818-x

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