The Optimality Conditions for Generalized Uniform η – V – I Invariant Convexity Programming

Abstract Generalized uniformly invariant convex programming is an important optimization problem that has numerous practical applications, such as transportation planning, engineering optimization, etc. The study of its optimal conditions can help solve practical problems and improve efficiency. Optimality conditions serve as the foundation of optimization theory by aiding in understanding the nature and characteristics of problems and providing guidance for the design and analysis of optimization algorithms. Therefore, studying the optimality conditions of generalized uniformly invariant convex programming is highly significant for solving practical problems, promoting the development of optimization theory and algorithm design and analysis, as well as fostering interdisciplinary research. In this research, a novel type of generalized uniform η-V-I invexity function is defined through the use of the η - subdifferential. In the case of the new generalized convex functions, a certain of multiobjective programming with this generalized convexity is discussed, and the corresponding sufficient optimality conditions are obtained.