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.

#### 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: https://hdl.handle.net/11571/210396
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