Titlebook: Introduction to Methods for Nonlinear Optimization; Luigi Grippo,Marco Sciandrone Textbook 2023 Springer Nature Switzerland AG 2023 Optimi

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Duality Theory,development of computational algorithms. In particular, after a short discussion on the general motivation of duality, we give some basic result on . and, under appropriate assumptions, we obtain new interpretations of the KKT multipliers. We also present the Wolfe’s duality theory, which is at the

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Optimality Conditions Based on Theorems of the Alternative,based on ., i.e., theorems stating that exactly one of two systems has solution. These latter are reported in the appendix where, in particular, optimality conditions for linear programming are proved using only an algebraic approach. We first consider problems with only inequality constraints and w

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Line Search Methods,rict our attention to .. . extensions will be considered in Chap. .. Here, after a short introduction, we first analyze methods employing derivatives of the objective function and then we describe some derivative-free extensions.

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Gradient Method,titutes the prototype of a globally convergent algorithm. In particular, here we consider the standard monotone version, also known as ., based on line searches, and a version with .. We prove global convergence and we report some estimates of the convergence rate. We show also that finite convergen

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Trust Region Methods, by minimizing a (possibly nonconvex) quadratic model of the objective function over a suitable neighborhood of the current point. Global convergence results are reported and methods for the solution of the constrained quadratic subproblem are described. We present a globalization strategy for Newto

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Methods for Nonlinear Equations, on the use of optimization techniques. In particular, we describe globalization algorithms that take into account the structure of the problem. Non monotone globalization techniques will be defined later.

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Derivative-Free Methods for Unconstrained Optimization,e consider unconstrained minimization problems and we describe some of the best known derivative-free methods. Then we study a class of globally convergent methods based on the inexact derivative-free linesearch techniques already introduced in Chap. .. Finally, we describe some techniques employing