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This research investigates necessary conditions of efficiency within a new multiobjective optimization framework.

April 30, 2026Mathematics0 citationsOpen Access

On Higher-Order PDE Constrained Multiobjective Optimization Models

STSavin TreanţăUniversity of Science and Technology OAOmar Mutab AlsalamiTaif University

Key Points

This research investigates necessary conditions of efficiency within a new multiobjective optimization framework.
Formulated a new class of multiobjective variational models.
Analyzed models governed by higher-order partial derivatives.
Applied techniques from variational calculus to derive main results.
Established conditions for efficiency in multiobjective optimization.
Examined vector-valued functionals defined by multiple integrals.
Characterized efficiency criteria within the proposed models.

Abstract

In this paper, we formulate and prove necessary conditions of efficiency for a new class of multiobjective variational models governed by higher order partial derivatives. More precisely, we consider a multiobjective optimization model of minimizing a vector of multiple integral functionals subject to certain higher order differential equations and/or inequations. The main results are derived by applying suitable techniques coming from variational calculus. The current contribution lies in vector-valued functionals given by multiple integrals, constraint coupling, and the characterization of efficiency criteria.

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