Optimality and solutions for conic robust multiobjective programs

Thai Doan Chuong (), Xinghuo Yu (), Andrew Eberhard (), Chaojie Li () and Chen Liu ()
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Thai Doan Chuong: Brunel University of London, Department of Mathematics
Xinghuo Yu: RMIT University, School of Engineering
Andrew Eberhard: RMIT University, School of Engineering
Chaojie Li: UNSW Sydney, School of Electrical Engineering and Telecommunications
Chen Liu: RMIT University, School of Engineering

Journal of Global Optimization, 2025, vol. 93, issue 3, No 5, 747-776

Abstract: Abstract This paper presents a robust framework for handling a conic multiobjective linear optimization problem, where the objective and constraint functions are involving affinely parameterized data uncertainties. More precisely, we examine optimality conditions and calculate efficient solutions of the conic robust multiobjective linear problem. We provide necessary and sufficient linear conic criteria for efficiency of the underlying conic robust multiobjective linear program. It is shown that such optimality conditions can be expressed in terms of linear matrix inequalities and second-order conic conditions for a multiobjective semidefinite program and a multiobjective second order conic program, respectively. We show how efficient solutions of the conic robust multiobjective linear problem can be found via its conic programming reformulation problems including semidefinite programming and second-order cone programming problems. Numerical examples are also provided to illustrate that the proposed conic programming reformulation schemes can be employed to find efficient solutions for concrete problems including those arisen from practical applications.

Keywords: Multiobjective optimization; Robust optimization; Efficient solution; Optimality condition; Conic reformulation; Semidefinite programming; 65K10; 49K99; 90C46; 90C29 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01552-y

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