{"product_id":"infinite-dimensional-optimization-and-control-theory-hardback-9780521451253","title":"Infinite Dimensional Optimization and Control Theory (Hardback) 9780521451253","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInfinite Dimensional Optimization and Control Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eTreats optimal problems for systems described by ODEs and PDEs, using an approach that unifies finite and infinite dimensional nonlinear programming.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eHector O. Fattorini (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521451253, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 28 March 1999\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e816 pages\u003cbr\u003e24.2 x 16.5 x 2.9 cm, 1.007 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eReview of the hardback: '… an impressive monograph on infinite dimensional optimal control theory. This is an original and extensive contribution which is not covered by other recent books in the control theory.' J. P. Raymond, Zentralblatt für Mathematik\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book is on existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from Kuhn–Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Evolution partial differential equations are studied using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart I. Finite Dimensional Control Problems: 1. Calculus of variations and control theory\u003cbr\u003e 2. Optimal control problems without target conditions\u003cbr\u003e 3. Abstract minimization problems: the minimum principle for the time optimal problem\u003cbr\u003e 4. Abstract minimization problems: the minimum principle for general optimal control problems\u003cbr\u003e Part II. Infinite Dimensional Control Problems: 5. Differential equations in Banach spaces and semigroup theory\u003cbr\u003e 6. Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems\u003cbr\u003e 7. Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations\u003cbr\u003e 8. Interpolation and domains of fractional powers\u003cbr\u003e 9. Linear control systems\u003cbr\u003e 10. Optimal control problems with state constraints\u003cbr\u003e 11. Optimal control problems with state constraints: The abstract parabolic case\u003cbr\u003e Part III. Relaxed Controls: 12. Spaces of relaxed controls: topology and measure theory\u003cbr\u003e 13. Relaxed controls in finite dimensional systems: existence theory\u003cbr\u003e 14. Relaxed controls in infinite dimensional spaces: existence theory.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Optimization [\u003ca title=\"See our other books on Optimization\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Optimization%20%5BPBU%5D%22\"\u003ePBU\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46007477993752,"sku":"9780521451253","price":145.45,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521451253i_95513f36-3cea-4fdb-9330-a9d2190bb24f.jpg?v=1691382216","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/infinite-dimensional-optimization-and-control-theory-hardback-9780521451253","provider":"Freshly Printed Books","version":"1.0","type":"link"}