{"title":"Optimization","description":"\u003cp\u003eOptimization in mathematics focuses on finding the best solution to a problem from a set of possible choices, using analytical and computational techniques. This area covers topics such as linear and nonlinear programming, constrained and unconstrained problems, numerical methods, and real-world applications in engineering, economics, and data science.\u003c\/p\u003e\u003cp\u003eTo deepen your understanding of optimization, consider narrowing your reading to areas like algorithm development, classical vs. modern optimization methods, or specific applications in industry. This subject stands apart from general mathematics by emphasizing strategic problem-solving and decision-making for efficient outcomes.\u003c\/p\u003e","products":[{"product_id":"continuous-optimization-data-science-9789819801503-new","title":"Continuous Optimization for Data Science","description":"\u003cp\u003eThe text is divided into three main parts: unconstrained optimization, constrained optimization, and linear programming. The first part addresses unconstrained optimization in single-variable and multivariable functions, introducing key algorithms such as steepest descent, Newton, and quasi-Newton methods.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe second part focuses on constrained optimization, starting with linear equality constraints and extending to more general cases, including inequality constraints. It details optimality conditions, sensitivity analysis, and relevant algorithms for solving these problems.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe third part covers linear programming, presenting the formulation of LP problems, the simplex algorithm, and sensitivity analysis. 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For dynamic situations, the author first recalls control theory which is treated as single-person differential games. Then a systematic theory of two-person differential games is concisely presented, including evasion and pursuit problems, zero-sum problems and LQ differential games.\u003c\/p\u003e\u003cp\u003eThe book is intended to be self-contained, assuming that the readers have basic knowledge of calculus, linear algebra, and elementary ordinary differential equations. The readership of the book could be junior\/senior undergraduate and graduate students with majors related to applied mathematics, who are interested in differential games. 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With this newly developed ACORN (Adaptive Constrained Optimal Robust Nonlinear) algorithm, it is possible to minimize the objective function [constructed from the functions in the nonlinear set of equations] without computing its derivatives.\u003c\/p\u003e\u003cp\u003eThis book will present the details of ACORN algorithm and how it is used to solve large scale nonlinear equations with an innovative approach ACORN Magic [minimization algorithms gathered in a cloud].\u003c\/p\u003e\u003cp\u003eThe ultimate motivation of this work is its application to optimization. In recent years, with the advances in big-data, optimization becomes an even more powerful tool in knowledge discovery. 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This book introduces some classical and basic results of optimization theory, including nonlinear programming with Lagrange multiplier method, the Karush-Kuhn-Tucker method, Fritz John's method, problems with convex or quasi-convex constraints, and linear programming with geometric method and simplex method.\u003c\/p\u003e\u003cp\u003eA slim book such as this which touches on major aspects of optimization theory will be very much needed for most readers. We present nonlinear programming, convex programming, and linear programming in a self-contained manner. This book is for a one-semester course for upper level undergraduate students or first\/second year graduate students. 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The richness and power of the theory are demonstrated by separate analyses of single-model and multi-modal repertoires, consisting of verities of estimation and control facets. Starting with purely mathematical concepts, specifically, abstract probability and information theories, model control theory is gradually revealed as a rather amazing domain. The mathematical equations, taking essentially simple forms, are exposed as powerful generators of motion. Moreover, seemingly obvious applications of the theory, such as high-performance aircraft control make room for unexpected virtual reality feedback in control of motion for the neurologically impaired.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eFollowing the presentation of some historical milestones and mathematical preliminaries, the book is divided into four parts. The first deals with minimal-order models of state estimation and control. 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While the clinical studies reported were all based on a single-model paradigm, a later reflection reveals that, given the variety of neurological symptoms associated with the relevant disorders, a multi-modal approach, as that addressed in the control of high-performance aircraft in a large flight envelope, would be similarly applicable in the treatment of neurological disorders.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544198480162,"sku":"9789811269578-new","price":135.28,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789811269578.jpg?v=1776399930"},{"product_id":"logic-third-9789811261015-new","title":"The Logic of the Third","description":"\u003cp\u003eThis book is a scientific basis for understanding the urgent need for a Great Transformation to a third step in social evolution. Already being a community of common destiny, humanity can form an actual unity through diversity to avoid extinction. Social actors can recognise informational imperatives for cognition, communication and co-operation to achieve such a unity. By doing so, they apply a logic that underlies the structuration of any agency, which is a real logic of self-organising systems from the physical to the social. This logic is the Logic of the Third - the Third is a meta-structure that emerges in a leap. The agents interact and when they co-act they are likely to form a real meta-structure of organisational relations. Informational agents anticipate this by generating requisite information in their attempt to cope with complex challenges. Such an information is a meta-structure too. 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