Optimization on Metric and Normed Spaces

The monograph is devoted to the study of optimization problems on complete metric spaces and Banach spaces. It contains a number of recent results
obtained by the author in the last ten years. It is a well-known fact that solutions exist for minimization problems on compact metric spaces with lower
semicontinuous objective functions. Solutions also exist for minimization problems on metric spaces such that all their bounded closed subsets are compact
if objective functions are lower semicontinuous and satisfy a coercivity growth condition. Since in the book we do not use compactness assumptions on spaces where optimization problems are considered the situation becomes more difficult. We overcome this difficulty in the following way: in Chapters 2 and 3 we deal with approximate solutions of optimization problems which always exist and in Chapters 4{10 we use the so-called generic approach which is applied fruitfully in many areas of Analysis (see, for example, [3, 74, 130] and the references mentioned there).