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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.
List 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.
About the author
Mishra, Shashi Kant; Upadhyay, Balendu Bhooshan
Summary
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.
Additional text
"This is a study of the mathematics of pseudolinear functions and their applications. … [The book includes] some applications of pseudolinear optimization problems to hospital management and economics."—Zentralblatt MATH 1326
"There is a real need for this book in the market. … There are numerous books on generalized convexity with applications, but there are only a few books concerned with pseudolinear functions. There are many books on nonconvex optimization with applications, but they do not contain pseudolinear functions. There are also several books on vector optimization, but they do not contain pseudolinear functions."—Nan-Jing Huang, Sichuan University, Chengdu, People’s Republic of China
