Optimality and scalarization of robust approximate solutions for semi-infinite vector equilibrium problems

• Published in: Journal of inequalities and applications Vol. 2025; no. 1; pp. 67 - 16
• Main Authors: Cai, Shan, Li, Xiaoping
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 03.06.2025; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; Clarke subdifferential; Cone strongly monotone function; Constraints; Control and Optimization in Sustainability Applications; Convexity; Equilibrium; Mathematical functions; Mathematical programming; Mathematics; Mathematics and Statistics; Monotone functions; Optimality condition; Optimization; Robustness (mathematics); Scalarization theorems; Semi-infinite vector equilibrium; Theorems; Semi-infinite vector equilibrium; Clarke subdifferential; Scalarization theorems; 90C46; Cone strongly monotone function; 90C25; 90C22; Optimality condition
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-025-03315-5

This paper investigates the optimality conditions and scalarization theorems for robust approximate solutions to semi-infinite vector equilibrium problems with data uncertainty in the constraints. Under suitable constraint qualifications, we establish a necessary optimality condition for robust approximate quasi-weakly efficient solutions using the Clarke subdifferential. Subsequently, we present a sufficient optimality condition for such solutions under the assumption of approximate generalized convexity. Finally, we formulate two scalarization theorems for robust approximate quasi-weakly efficient solutions by employing a cone-strongly monotonic function. The definitions and main conclusions of this paper are supported by specific examples.