{"product_id":"lagrange-multiplier-approach-to-variational-problems-and-applications-paperback-softback-9780898716498","title":"Lagrange Multiplier Approach to Variational Problems and Applications (Paperback \/ softback) 9780898716498","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLagrange Multiplier Approach to Variational Problems and Applications\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAnalyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eKazufumi Ito (Author), Karl Kunisch (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780898716498\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 30 July 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e359 pages\u003cbr\u003e25.5 x 18 x 2 cm, 0.658 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis comprehensive monograph analyses Lagrange multiplier theory, which provides a tool for the analysis of a general class of nonlinear variational problems, and is the basis for developing efficient and powerful iterative methods for solving these problems. This book shows its impact on the development of numerical algorithms for problems posed in a function space setting, and is motivated by the idea that a full treatment of a variational problem in function spaces would be incomplete without a discussion of infinite-dimensional analysis, proper discretisation, and the relationship between the two. The authors develop and analyse efficient algorithms for constrained optimisation and convex optimisation problems based on the augmented Lagrangian concept and cover such topics as sensitivity analysis and convex optimisation. General theory is applied to challenging problems in optimal control of partial differential equations, image analysis, mechanical contact and friction problems, and American options for the Black–Scholes model.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e 1. Existence of Lagrange multipliers\u003cbr\u003e 2. Sensitivity analysis\u003cbr\u003e 3. First Order augmented Lagrangians for equality and finite rank inequality constraints\u003cbr\u003e 4. Augmented Lagrangian methods for nonsmooth, convex optimization\u003cbr\u003e 5. Newton and SQP methods\u003cbr\u003e 6. Augmented Lagrangian-SQP methods\u003cbr\u003e 7. The primal-dual active set method\u003cbr\u003e 8. Semismooth Newton methods I\u003cbr\u003e 9. Semismooth Newton methods II: applications\u003cbr\u003e 10. Parabolic variational inequalities\u003cbr\u003e 11. Shape optimization\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Miscellaneous items [\u003ca title=\"See our other books on Miscellaneous items\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Miscellaneous%20items%20%5BWZ%5D%22\"\u003eWZ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"MP–SIA SIAM – Society for Industrial and Applied M","offers":[{"title":"Brand New","offer_id":52410747617560,"sku":"9780898716498","price":83.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780898716498i.jpg?v=1784251377","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/lagrange-multiplier-approach-to-variational-problems-and-applications-paperback-softback-9780898716498","provider":"Freshly Printed Books","version":"1.0","type":"link"}