Convergence of a new logarithmic penalty function for nonlinear multiobjective optimization problems with equality constraints
Optimization Eruditorum, Volume 3, Issue 2, August 2026, Pages 86–107
ABDOULAYE COMPAORÉ
Laboratoire de Mathématiques, Informatique et Applications, Université Norbert Zongo, RN14 Koudougou, Burkina Faso
ALEXANDRE SOM
Département de Mathématiques, Physique et Chimie, Université Peleforo Gon Coulibaly, BP~1328 Korhogo, Côte d'Ivoire
RÉMI GUILLAUME BAGRÉ
Laboratoire de Mathématiques, Informatique et Applications, Université Norbert Zongo, RN14 Koudougou, Burkina Faso
Abstract
This article presents an extension of the logarithmic penalization technique for nonlinear multiobjective optimization problems with equality constraints. The proposed penalty function is distinct from existing ones: it is regular and satisfies an asymptotic exactness property (in the sense that penalized Pareto sets converge to those of the original problem as the penalty parameter grows), provided the constraint and objective functions are continuously differentiable. We establish the theoretical foundations of this extension and study the convergence of the technique toward Pareto optimal solutions, focusing on two types: weakly Pareto optimal solutions and Pareto optimal solutions. The convergence analysis rests on two key lemmas characterizing the asymptotic behavior of the penalty term on and outside the feasible set as the penalty parameter grows. We show that the limit superior and limit inferior of the penalized solution sets are both contained in the feasible domain, and that no accumulation point lies outside the true Pareto sets of the original problem. We also study the method combined with the augmented weighted Chebyshev distance, which scalarizes the penalized problem and simplifies the search for Pareto solutions, establishing equivalence between Pareto optimal solutions of the penalized problem and minimizers of the Chebyshev scalarization. The theoretical results confirm that the proposed logarithmic penalization converges correctly in determining Pareto solutions for nonlinear multiobjective optimization problems with equality constraints.
Cite this Article as
A. Compaoré, A. Som and R. G. Bagré, convergence of a new logarithmic penalty function for nonlinear multiobjective optimization problems with equality constraints, Optimization Eruditorum, 3(2), 86–107, 2026