Work

The projected gradient direction in vector optimization: continuity and dual characterization

Year: 2026

Type: article

Abstract: This technical note proves that, for a smooth vector optimization problem on a closed convex feasible set ordered by a pointed cone, the projected gradient direction depends continuously on the decision variable. Our argument is based on a simple and direct proof via a fixed-domain reformulation of the subproblem. We then give a necessary and sufficient dual characterization of this direction and show that its associated set-valued dual variable mapping is outer semicontinuous.

Source: Computational and Applied Mathematics

DOI: 10.1007/s40314-025-03611-2

Authors: N. Fazzio, L. F. Prudente, M. L. Schuverdt

Institutions: Universidad Nacional de La Plata, Universidade Federal de Goiás

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Consejo Nacional de Investigaciones Científicas y Técnicas, Conselho Nacional de Desenvolvimento Científico e Tecnológico