The book presents an overview (and also some new results) on invex and related functions in various types of optimization problems (with single-valued objective functions, with vector-valued objective functions, and static as well as dynamic problems). The content of the book is structured as follows. Chapter 1 is an introduction, where the authors give the basic notions of convexity and generalized convexity in the finite-dimensional real space $\Bbb{R}^n$Rn. Chapter 2 is devoted to a discussion on the definition and meaning of invexity in the differentiable case. A comparison of invexity with other concepts of generalized convexity is also given. Chapter 3 deals with $\eta$η-pseudolinear ($f$f and $-f$−f both pseudo-invex) functions and the links between invexity and generalized monotonicity. Chapter 4 is concerned with invexity for non-smooth functions; in particular, with the Lipschitzian case using Clarke's theory of generalized gradients. Chapter 5 discusses invexity in nonlinear programming and examines the relevant role of invexity to duality theory. In Chapter 6, the authors consider a multiobjective optimization problem involving invex functions and present several duality results for multiobjective programming problems. Chapter 7 is devoted to some variational and control optimization problems. Finally, in Chapter 8, several applications of invexity to special optimization problems are presented (problems with quadratic functions, fractional programming problems, non-differentiable programs, etc.).

Invexity and optimization.

GIORGI, GIORGIO
2008

Abstract

The book presents an overview (and also some new results) on invex and related functions in various types of optimization problems (with single-valued objective functions, with vector-valued objective functions, and static as well as dynamic problems). The content of the book is structured as follows. Chapter 1 is an introduction, where the authors give the basic notions of convexity and generalized convexity in the finite-dimensional real space $\Bbb{R}^n$Rn. Chapter 2 is devoted to a discussion on the definition and meaning of invexity in the differentiable case. A comparison of invexity with other concepts of generalized convexity is also given. Chapter 3 deals with $\eta$η-pseudolinear ($f$f and $-f$−f both pseudo-invex) functions and the links between invexity and generalized monotonicity. Chapter 4 is concerned with invexity for non-smooth functions; in particular, with the Lipschitzian case using Clarke's theory of generalized gradients. Chapter 5 discusses invexity in nonlinear programming and examines the relevant role of invexity to duality theory. In Chapter 6, the authors consider a multiobjective optimization problem involving invex functions and present several duality results for multiobjective programming problems. Chapter 7 is devoted to some variational and control optimization problems. Finally, in Chapter 8, several applications of invexity to special optimization problems are presented (problems with quadratic functions, fractional programming problems, non-differentiable programs, etc.).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11571/210396
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