Pseudolinear Functions and Optimization

This is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. The book discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems. It encompasses nearly all the published literature on the subject along with new results on semi-infinite nonlinear programming problems. The authors present optimality conditions and duality results for many types of optimization problems. They also extend pseudolinear functions to higher-level problems and explore applications to hospital management and economics.

Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems.

The book describes the characterizations of solution sets of various optimization problems. It examines multiobjective pseudolinear, multiobjective fractional pseudolinear, static minmax pseudolinear, and static minmax fractional pseudolinear optimization problems and their results. The authors extend these results to locally Lipschitz functions using Clarke subdifferentials. They also present optimality and duality results for h-pseudolinear and semi-infinite pseudolinear optimization problems.

The authors go on to explore the relationships between vector variational inequalities and vector optimization problems involving pseudolinear functions. They present characterizations of solution sets of pseudolinear optimization problems on Riemannian manifolds as well as results on pseudolinearity of quadratic fractional functions. The book also extends n-pseudolinear functions to pseudolinear and n-pseudolinear fuzzy mappings and characterizations of solution sets of pseudolinear fuzzy optimization problems and n-pseudolinear fuzzy optimization problems. The text concludes with some applications of pseudolinear optimization problems to hospital management and economics.

This book encompasses nearly all the published literature on the subject along with new results on semi-infinite nonlinear programming problems. It will be useful to readers from mathematical programming, industrial engineering, and operations management.