A first course in optimization. (2014)

• Record Type: Book
• Further Information: Note: Charles L. Byrne.
• Authors: Byrne, Charles L, 1947-
• Contents: Optimization without Calculus; Chapter Summary; The Arithmetic Mean-Geometric Mean Inequality; An Application of the AGM Inequality: the Number e; Extending the AGM Inequality; Optimization Using the AGM Inequality; The Holder and Minkowski Inequalities; Cauchy's Inequality; Optimizing using Cauchy's Inequality; An Inner Product for Square Matrices; Discrete Allocation Problems Geometric Programming; Chapter Summary; An Example of a GP Problem; Posynomials and the GP Problem; The Dual GP Problem; Solving the GP Problem; Solving the DGP Problem; Constrained Geometric Programming Basic Analysis; Chapter Summary; Minima and Infima; Limits; Completeness; Continuity; Limsup and Liminf; Another View; Semi-Continuity Convex Sets; Chapter Summary; The Geometry of Real Euclidean Space; A Bit of Topology; Convex Sets in RJ ; More on Projections; Linear and Affine Operators on RJ; The Fundamental Theorems; Block-Matrix Notation; Theorems of the Alternative; Another Proof of Farkas' Lemma; Gordan's Theorem Revisited Vector Spaces and Matrices; Chapter Summary; Vector Spaces; Basic Linear Algebra; LU and QR Factorization; The LU Factorization Linear Programming; Chapter Summary; Primal and Dual; Converting a Problem to PS Form; Duality Theorems; The Basic Strong Duality Theorem; Another Proof; Proof of Gale's Strong Duality Theorem; Some Examples; The Simplex Method; Yet Another Proof; The Sherman–Morrison–Woodbury Identity; An Example of the Simplex Method; Another Example; Some Possible Difficulties; Topics for Projects Matrix Games and Optimization; Chapter Summary; Two-Person Zero-Sum Games; Deterministic Solutions; Randomized Solutions ; Symmetric Games; Positive Games; Example: The "Bluffing" Game; Learning the Game; Non-Constant-Sum Games Differentiation; Chapter Summary; Directional Derivative; Partial Derivatives; Some Examples; Gâteaux Derivative; Fréchet Derivative; The Chain Rule Convex Functions; Chapter Summary; Functions of a Single Real Variable; Functions of Several Real Variables; Sub-Differentials and Sub-Gradients; Sub-Gradients and Directional Derivatives; Functions and Operators; Convex Sets and Convex Functions Convex Programming; Chapter Summary; The Primal Problem; From Constrained to Unconstrained; Saddle Points; The Karush–Kuhn–Tucker Theorem; On Existence of Lagrange Multipliers; The Problem of Equality Constraints; Two Examples; The Dual Problem; Nonnegative Least-Squares Solutions; An Example in Image Reconstruction; Solving the Dual Problem; Minimum One-Norm Solutions Iterative Optimization; Chapter Summary; The Need for Iterative Methods; Optimizing Functions of a Single Real Variable; The Newton–Raphson Approach; Approximate Newton–Raphson Methods; Derivative-Free Methods; Rates of Convergence; Descent Methods; Optimizing Functions of Several Real Variables; Auxiliary-Function Methods; Projected Gradient-Descent Methods; Feasible-Point Methods; Quadratic Programming; Simulated Annealing Solving Systems of Linear Equations; Chapter Summary; Arbitrary Systems of Linear Equations; Regularization; Nonnegative Systems of Linear Equations; Regularized SMART and EMML; Block-Iterative Methods Conjugate-Direction Methods; Chapter Summary; Iterative Minimization; Quadratic Optimization; Conjugate Bases for RJ; The Conjugate Gradient Method; Krylov Subspaces; Extensions of the CGM Operators ; Chapter Summary; Operators; Contraction Operators; Orthogonal-Projection Operators; Two Useful Identities; Averaged Operators; Gradient Operators; Affine-Linear Operators; Paracontractive Operators; Matrix Norms Looking Ahead; Chapter Summary; Sequential Unconstrained Minimization; Examples of SUM; Auxiliary-Function Methods; The SUMMA Class of AF Methods Bibliography Index Exercises appear at the end of each chapter.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2014
• Extent: 1 online resource
• Subjects: 519.6; Mathematical optimization
• Languages: English
• ISBNs: 9781482226607; 9781482226584; 9781482226591
• Related ISBNs: 9781482226560
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
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