{"product_id":"the-linearization-method-for-constrained-b-n-pshenichnyi-9783540570370","title":"The Linearization Method for Constrained Optimization","description":"1. Convex and Quadratic Programming.- 1.1 Introduction.- 1.1.1 The Linearization Algorithm.- 1.1.2 Convergence of the Algorithm.- 1.1.3 General Remarks.- 1.1.4 Notation.- 1.2 Necessary Conditions for a Minimum and Duality.- 1.2.1 Convex Sets.- 1.2.2 Convex Functions.- 1.2.3 Foundations of Convex Programming.- 1.2.4 Duality in Convex Programming.- 1.2.5 Necessary Conditions for Extrema. General Problem.- 1.2.6 Necessary Conditions for Extrema: Second Order Conditions . ..- 1.2.7 Minimax Problems.- 1.2.8 Penalty Functions.- 1.3 Quadratic Programming Problems.- 1.3.1 Conjugate Gradient Method.- 1.3.2 Conjugate Gradient Algorithm.- 1.3.3 Existence of a Solution.- 1.3.4 Necessary Conditions for an Extremum and the Dual Problem.- 1.3.5 Application, Projection onto a Subspace.- 1.3.6 Algorithm for the Quadratic Programming Problem.- 1.3.7 Computational Aspects.- 1.3.8 Algorithms for Simple Constraints. Generalization.- 2. The Linearization Method.- 2.1 The General Algorithm.- 2.1.1 Main Assumptions.- 2.1.2 Formulation of the Algorithm.- 2.1.3 Convergence of the Algorithm.- 2.1.4 Computational Aspects.- 2.1.5 Generalizations.- 2.1.6 The Linear Programming Problem.- 2.1.7 The Linearization Method with Equality-Type Constraints.- 2.1.8 Simple Constraints.- 2.1.9 Choice of Parameters in the Linearization Method. Modified Algorithm.- 2.2 Resolution of Systems of Equations and Inequalities.- 2.2.1 The Auxiliary Problem.- 2.2.2 The Algorithm.- 2.2.3 Convergence of the Algorithm.- 2.3 Acceleration of the Convergence of the Linearization Method.- 2.3.1 Main Assumptions.- 2.3.2 Local Analysis of the Auxiliary Problem.- 2.3.3 Preliminary Lemmas.- 2.3.4 The Linearization Algorithm and Acceleration of Convergence.- 2.3.5 Linear Transformations of the Problem.- 2.3.6 Modifications of the Linearization Method.- 3. The Discrete Minimax Problem and Algorithms.- 3.1 The Discrete Minimax Problem.- 3.1.1 The Auxiliary Problem.- 3.1.2 Some Bounds.- 3.1.3 Algorithms.- 3.1.4 Algorithm for Ak =In.- 3.1.5 Acceleration of Convergence in the Convex Case.- 3.2 The Dual Algorithm for Convex Programming Problems.- 3.2.1 The Dual Algorithm.- 3.2.2 Bounds on the Rate of Convergence.- 3.2.3 An Algorithm for Convex Programming Problems.- 3.3 Algorithms and Examples.- 3.3.1 The Linearization Method.- 3.3.2 The Accelerated Linearization Method.- 3.3.3 Examples of Calculations.- Appendix: Comments on the Literature.- References.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e B. N. Pshenichnyi, Boris N. Pshenichnyj\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3540570373\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783540570370\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 04\/28\/1994\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 164\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.90lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.44d","brand":"B. N. Pshenichnyi","offers":[{"title":"Hardcover","offer_id":44149092319487,"sku":"9783540570370","price":99.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_2be3b75f-0437-4014-ac6e-973505ea6751.jpg?v=1688454793","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-linearization-method-for-constrained-b-n-pshenichnyi-9783540570370","provider":"WR Book House","version":"1.0","type":"link"}