Well-Posed Optimization Problems
Dontchev, Asen L.
Well-Posed Optimization Problems [electronic resource] / by Asen L. Dontchev, Tullio Zolezzi. - XII, 424 p. online resource. - Lecture Notes in Mathematics, 1543 0075-8434 ; . - Lecture Notes in Mathematics, 1543 .
Tykhonov well-posedness -- Hadamard and tykhonov well-posedness -- Generic well-posedness -- Well-posedness and variational, epi- and mosco convergences -- Well-posedness in optimal control -- Relaxation and value hadamard well-posedness in optimal control -- Singular perturbations in optimal control -- Well-posedness in the calculus of variations -- Hadamard well-posedness in mathematical programming.
This book presents in a unified way the mathematical theory of well-posedness in optimization. The basic concepts of well-posedness and the links among them are studied, in particular Hadamard and Tykhonov well-posedness. Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming are considered. Both the pure and applied side of these topics are presented. The main subject is often introduced by heuristics, particular cases and examples. Complete proofs are provided. The expected knowledge of the reader does not extend beyond textbook (real and functional) analysis, some topology and differential equations and basic optimization. References are provided for more advanced topics. The book is addressed to mathematicians interested in optimization and related topics, and also to engineers, control theorists, economists and applied scientists who can find here a mathematical justification of practical procedures they encounter.
9783540476443
10.1007/BFb0084195 doi
Systems theory.
Mathematical optimization.
Economic theory.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Economic Theory/Quantitative Economics/Mathematical Methods.
Q295 QA402.3-402.37
519
Well-Posed Optimization Problems [electronic resource] / by Asen L. Dontchev, Tullio Zolezzi. - XII, 424 p. online resource. - Lecture Notes in Mathematics, 1543 0075-8434 ; . - Lecture Notes in Mathematics, 1543 .
Tykhonov well-posedness -- Hadamard and tykhonov well-posedness -- Generic well-posedness -- Well-posedness and variational, epi- and mosco convergences -- Well-posedness in optimal control -- Relaxation and value hadamard well-posedness in optimal control -- Singular perturbations in optimal control -- Well-posedness in the calculus of variations -- Hadamard well-posedness in mathematical programming.
This book presents in a unified way the mathematical theory of well-posedness in optimization. The basic concepts of well-posedness and the links among them are studied, in particular Hadamard and Tykhonov well-posedness. Abstract optimization problems as well as applications to optimal control, calculus of variations and mathematical programming are considered. Both the pure and applied side of these topics are presented. The main subject is often introduced by heuristics, particular cases and examples. Complete proofs are provided. The expected knowledge of the reader does not extend beyond textbook (real and functional) analysis, some topology and differential equations and basic optimization. References are provided for more advanced topics. The book is addressed to mathematicians interested in optimization and related topics, and also to engineers, control theorists, economists and applied scientists who can find here a mathematical justification of practical procedures they encounter.
9783540476443
10.1007/BFb0084195 doi
Systems theory.
Mathematical optimization.
Economic theory.
Systems Theory, Control.
Calculus of Variations and Optimal Control; Optimization.
Economic Theory/Quantitative Economics/Mathematical Methods.
Q295 QA402.3-402.37
519