{"product_id":"infinite-dimensional-optimization-and-control-theory-advanced-pde","title":"Infinite Dimensional Optimization and Control Theory - Advanced PDE","description":"\u003cp\u003eIn this review of Infinite Dimensional Optimization and Control Theory the bottom line is clear: this is an advanced, rigorous reference for researchers and graduate students working on optimal control of differential equations. The book's greatest virtue is its unified derivation of necessary conditions, including Pontryagin's maximum principle, from Kuhn-Tucker theorems in infinite dimensional settings, making it valuable for anyone needing a functional-analytic approach to control problems. Readers seeking practical, computational examples may find it less geared to numerical implementation and more focused on theoretical foundations.\u003c\/p\u003e\n\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eDerivation of necessary conditions:\u003c\/strong\u003e The author develops Pontryagin-type maximum principles from Kuhn-Tucker results, giving a coherent path from nonlinear programming to control theory.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eWide equation coverage:\u003c\/strong\u003e The text treats both ordinary and partial differential equations, so readers get methods applicable across finite and infinite dimensional dynamics.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTreatment of constraints:\u003c\/strong\u003e Control constraints, state constraints and target conditions are addressed explicitly, which helps when modeling realistic constrained control problems.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFunctional-analytic tools:\u003c\/strong\u003e Semigroup theory and abstract differential equation frameworks let the reader handle evolution PDEs in a systematic way.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eExistence theory for controls:\u003c\/strong\u003e A general theory of relaxed controls is presented to establish existence of optimal controls for arbitrary control sets.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eConnections with interpolation and integral equations:\u003c\/strong\u003e The inclusion of interpolation theory and integral equations broadens the analytical toolkit available to the reader.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis book is aimed primarily at graduate students, mathematicians and control theorists who need a rigorous, abstract treatment of optimal control for systems governed by ordinary and partial differential equations. It works well as a reference for researchers proving existence and necessary condition results or for instructors of advanced courses in control theory.\u003c\/p\u003e\n\u003cp\u003eThose looking for step-by-step numerical algorithms, software-oriented guidance, or an elementary introduction to control should look elsewhere, since the emphasis here is on rigorous proofs, functional analysis and the derivation of theoretical conditions rather than computational recipes.\u003c\/p\u003e\n\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eComprehensive theoretical derivations link Kuhn-Tucker theorems to Pontryagin-type conditions in infinite dimensional spaces.\u003c\/li\u003e\n\u003cli\u003eCareful treatment of evolution PDEs using semigroup theory gives a clear abstract framework for applications.\u003c\/li\u003e\n\u003cli\u003eThe relaxed control existence theory allows treatment of arbitrary control sets, useful for constrained problems.\u003c\/li\u003e\n\u003cli\u003eIncludes auxiliary tools like interpolation theory and integral equation approaches that support broader analysis.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eNot targeted at practitioners seeking numerical methods or software implementations; it is primarily theoretical.\u003c\/li\u003e\n\u003c\/ul\u003e\n\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eInfinite Dimensional Optimization and Control Theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eEncyclopedia of Mathematics and its Applications, Series Number 62\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eHector O. Fattorini\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eScope\u003c\/td\u003e\n\u003ctd\u003eOptimal control for ordinary and partial differential equations\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eKey methods\u003c\/td\u003e\n\u003ctd\u003eKuhn-Tucker theorems, Pontryagin maximum principle, semigroup theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eTopics covered\u003c\/td\u003e\n\u003ctd\u003eControl constraints, state constraints, target conditions, relaxed controls\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eInfinite Dimensional Optimization and Control Theory is a strong, mathematically rigorous reference for those proving existence and necessary condition results in control problems for ODEs and PDEs. It is good value for mathematicians and advanced students who need a systematic, abstract treatment; readers focused on computation should pair it with a numerical control text.\u003c\/p\u003e\n\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this book cover Pontryagin's maximum principle?\u003c\/strong\u003e\u003cbr\u003eYes, the book derives Pontryagin-type necessary conditions from Kuhn-Tucker theorems in infinite dimensional settings.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAre numerical methods and implementation details included?\u003c\/strong\u003e\u003cbr\u003eNo, the emphasis is theoretical and analytic; practical numerical algorithms are not the focus.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs the book suitable for PDE control problems?\u003c\/strong\u003e\u003cbr\u003eYes, it treats evolution partial differential equations using semigroup theory and related abstract tools.\u003c\/p\u003e","brand":"Hector O. 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