Numerical Optimization with Computational ErrorsThis book studies the approximate solutions of optimization problems in the presence of computational errors. A number of results are presented on the convergence behavior of algorithms in a Hilbert space; these algorithms are examined taking into account computational errors. The author illustrates that algorithms generate a good approximate solution, if computational errors are bounded from above by a small positive constant. Known computational errors are examined with the aim of determining an approximate solution. Researchers and students interested in the optimization theory and its applications will find this book instructive and informative.
This monograph contains 16 chapters; including a chapters devoted to the subgradient projection algorithm, the mirror descent algorithm, gradient projection algorithm, the Weiszfelds method, constrained convex minimization problems, the convergence of a proximal point method in a Hilbert space, the continuous subgradient method, penalty methods and Newton’s method.

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Contents
1  
11  
3 The Mirror Descent Algorithm  41 
4 Gradient Algorithm with a Smooth Objective Function  59 
5 An Extension of the Gradient Algorithm  73 
6 Weiszfelds Method  85 
7 The Extragradient Method for Convex Optimization  105 
8 A Projected Subgradient Method for Nonsmooth Problems  119 
11 Maximal Monotone Operators and the Proximal Point Algorithm  169 
12 The Extragradient Method for Solving Variational Inequalities  183 
13 A Common Solution of a Family of Variational Inequalities  205 
14 Continuous Subgradient Method  225 
15 Penalty Methods  239 
16 Newtons Method  265 
297  
302  
9 Proximal Point Method in Hilbert Spaces  137 
10 Proximal Point Methods in Metric Spaces  149 