Solving Two-stage Quadratic Multiobjective Problems via Optimality and Relaxations

Thai Doan Chuong (), Xinghuo Yu (), Chen Liu (), Andrew Eberhard () and Chaojie Li ()
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Thai Doan Chuong: Brunel University London
Xinghuo Yu: RMIT University
Chen Liu: RMIT University
Andrew Eberhard: RMIT University
Chaojie Li: UNSW Sydney

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 25, 676-713

Abstract: Abstract This paper focuses on the study of robust two-stage quadratic multiobjective optimization problems. We formulate new necessary and sufficient optimality conditions for a robust two-stage multiobjective optimization problem. The obtained optimality conditions are presented by means of linear matrix inequalities and thus they can be numerically validated by using a semidefinite programming problem. The proposed optimality conditions can be elaborated further as second-order conic expressions for robust two-stage quadratic multiobjective optimization problems with separable functions and ellipsoidal uncertainty sets. We also propose relaxation schemes for finding a (weak) efficient solution of the robust two-stage multiobjective problem by employing associated semidefinite programming or second-order cone programming relaxations. Moreover, numerical examples are given to demonstrate the solution variety of our flexible models and the numerical verifiability of the proposed schemes.

Keywords: Multiobjective optimization; Two-stage program; Semidefinite programming; Optimality condition; Relaxation problem; Pareto/efficient solution; 49K99; 65K10; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02528-w

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