{"product_id":"optimality-conditions-abnormal-and-degenerate-problems-rigorous","title":"Optimality Conditions: Abnormal and Degenerate Problems - Rigorous","description":"\u003cp\u003eIn this review of Optimality Conditions: Abnormal and Degenerate Problems the author presents a focused, rigorous treatment aimed squarely at readers who already work with variational and optimization theory; the single biggest reason to buy is the book's depth in necessary and sufficient extremality conditions, making it a valuable reference rather than an introductory textbook. This review examines the structure and intended audience, and explains why the book serves well as a graduate-level companion for mathematicians and researchers dealing with constrained minimization and optimal control.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive chapter layout:\u003c\/strong\u003e Four chapters guide the reader from abstract minimization with constraints through optimal control to integral quadratic forms and local properties, providing a clear roadmap for advanced study.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eFocused theory on extremality:\u003c\/strong\u003e The book concentrates on necessary and sufficient conditions, which helps researchers apply sharp theoretical tools to detect and classify extremal solutions.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eApplications to optimal control:\u003c\/strong\u003e A dedicated chapter on optimal control connects abstract results to one of the main applied classes of extremal problems.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eTreatment of calculus of variations objects:\u003c\/strong\u003e The chapter on integral quadratic forms offers detailed discussion of a central object in variational analysis used in stability and second variation arguments.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eDesigned for advanced readers:\u003c\/strong\u003e The text is organized for mathematicians, advanced students, and post-graduates seeking depth rather than elementary introductions, making study and research more efficient.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThe book is best for graduate students, post-graduate researchers, and professional mathematicians working in optimization, calculus of variations, and optimal control who need a concentrated presentation of extremality conditions. It is especially useful for those seeking a reference that treats abnormal and degenerate cases with mathematical rigor.\u003c\/p\u003e\n\u003cp\u003eThose new to optimization, or readers looking for applied numerical methods and step-by-step algorithmic guidance, should look elsewhere; this work assumes familiarity with advanced mathematical concepts and focuses on theoretical development rather than computational practice.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eDeep theoretical coverage of necessary and sufficient extremality conditions useful for rigorous proofs and research.\u003c\/li\u003e\n\u003cli\u003eDedicated chapters provide structured treatment of abstract minimization, optimal control, and integral quadratic forms.\u003c\/li\u003e\n\u003cli\u003eWritten to support advanced study, making it suitable as a reference for specialists and doctoral candidates.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eNot intended as an introductory text; readers without background in advanced analysis or variational methods will struggle.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eOptimality Conditions: Abnormal and Degenerate Problems\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSeries\u003c\/td\u003e\n\u003ctd\u003eMathematics and Its Applications\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthor\u003c\/td\u003e\n\u003ctd\u003eA.V. V. Arutyunov\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eStructure\u003c\/td\u003e\n\u003ctd\u003eFour chapters covering abstract minimization, optimal control, integral quadratic forms, and local properties\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAudience\u003c\/td\u003e\n\u003ctd\u003eMathematicians, advanced students, post-graduates, researchers\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eOptimality Conditions: Abnormal and Degenerate Problems is a compact, rigorous resource for specialists who need a concentrated exposition of extremality conditions, particularly in optimal control and the calculus of variations. It represents good value as a reference for graduate-level study and research, but it is not a substitute for introductory texts or computational guides.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eIs this book suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo. It assumes a strong background in advanced analysis and variational methods and is aimed at graduate-level readers and researchers.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eDoes it cover optimal control?\u003c\/strong\u003e\u003cbr\u003eYes. One chapter is devoted specifically to optimal control and connects general extremality results to that class of problems.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWill this help with practical numerical methods?\u003c\/strong\u003e\u003cbr\u003eThe focus is theoretical; readers looking for numerical algorithms or implementation guidance should consult applied optimization texts instead.\u003c\/p\u003e","brand":"A.V. V. Arutyunov","offers":[{"title":"Default Title","offer_id":48243459883227,"sku":"9048155967","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/51MqM5B3xZL._SL1187.jpg?v=1770996220","url":"https:\/\/gearmusthave.com\/products\/optimality-conditions-abnormal-and-degenerate-problems-rigorous","provider":"GearMustHave","version":"1.0","type":"link"}