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Optimality and Exact Moment-SDP Formulations for Robust Two-Stage Convex Polynomial Multiobjective Optimization
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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BibTeX
@misc{jiang2026optimality,
title = {{Optimality and Exact Moment-SDP Formulations for Robust Two-Stage Convex Polynomial Multiobjective Optimization}},
author = {Yongqi Jiang and Zhe Hong and Chengmiao Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39383},
eprint = {2610.39383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39383},
}
RIS
TY - UNPB
TI - Optimality and Exact Moment-SDP Formulations for Robust Two-Stage Convex Polynomial Multiobjective Optimization
AU - Yongqi Jiang
AU - Zhe Hong
AU - Chengmiao Yang
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39383
UR - https://arxiv.org/abs/2610.39383
AB - 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.
ER -