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This research aims to develop a straightforward dual problem for primal vector optimization using duality theory.

August 6, 2026TopOpen Access

Surrogate duality for quasiconvex vector minimization

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This research aims to develop a straightforward dual problem for primal vector optimization using duality theory.
Constructed a dual problem by analyzing the structure of the primal vector optimization problem.
Introduced nonlinear scalarization to compute the dual image set with a linear inequality constraint.
Defined upper semicontinuity for vector-valued functions and examined duality statements.
Established weak and strong duality conditions assuming D-quasiconvexity and D-upper semicontinuity of the objective function.
Demonstrated the feasibility of deriving a dual problem that is simpler and manageable.
Investigated specific scenarios to illustrate the application of the proposed duality.

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Randomized trial examines dual problem solutions in vector optimization, suggesting new methodologies.

Martínez-Legaz et al. (2026) studied this question.

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