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arXiv · 2610.39383

Optimality and Exact Moment-SDP Formulations for Robust Two-Stage Convex Polynomial Multiobjective Optimization

Yongqi Jiang·Zhe Hong·Chengmiao Yang
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Abstract

In this paper, we study Geoffrion properly efficient solutions of affinely adjustable robust two-stage convex polynomial multiobjective optimization problems with spectrahedral uncertainty. For convex polynomial data, we establish sufficient optimality conditions and necessary conditions under a Slater condition. Under SOS-convexity, we obtain an exact SOS characterization of proper efficiency. Using strictly positive weighted-sum scalarization, we develop a finite-dimensional moment-SDP formulation and establish its optimal-value exactness under the strict feasibility condition. We further establish the recovery results connecting Geoffrion properly efficient solutions with moment-SDP optimal solutions.

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Yongqi Jiang, Zhe Hong, Chengmiao Yang. 2026-10-29. Optimality and Exact Moment-SDP Formulations for Robust Two-Stage Convex Polynomial Multiobjective Optimization. https://arxiv.org/abs/2610.39383

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