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.
Table of Contents
Introduction. Pseudolinear Functions: Characterizations and Properties. Constrained Pseudolinear Optimization Problems: Characterizations of Solution Sets. Constrained Pseudolinear Optimization Problems: Characterizations of Solutions Sets in Terms of Lagrange Multipliers. Pseudolinear Multiobjective Optimization. Nonsmooth Pseudolinear Multiobjective Optimization. Static Minimax Programming and Pseudolinear Functions. Nonsmooth Static Minimax Programming and Pseudolinear Functions. Nonsmooth Multiobjective Pseudolinear Programming: Optimality and Duality in Terms of Bifunctions. Pseudolinear Multiobjective Semi-Infinite Programming Problems. Vector Variational Inequality and Vector Pseudolinear Optimization Problems. Extension of Pseudolinear Functions and Variational Inequality Problems. Ƞ Pseudolinear Functions: Characterizations and Properties of Solution Set. Smooth Pseudolinear Functions and Riemannian Manifolds. Pseudolinear Quadratic Fractional Functions. Pseudolinear Fuzzy Mapping. Pseudolinear Function and Its Applications.
Mishra, Shashi Kant; Upadhyay, Balendu Bhooshan