Linear and Convex Optimization. Michael H. Veatch

Linear and Convex Optimization - Michael H. Veatch


Скачать книгу
ection id="u62afbcc0-91c9-5c27-8f72-256199ed5c3d">

      Table of Contents

      1  Cover

      2  Linear and Convex Optimization

      3  Copyright

      4  Preface

      5  About the Companion Website

      6  1 Introduction to Optimization Modeling 1.1 Who Uses Optimization? 1.2 Sending Aid to a Disaster 1.3 Optimization Terminology 1.4 Classes of Mathematical Programs

      7  2 Linear Programming Models 2.1 Resource Allocation 2.2 Purchasing and Blending 2.3 Workforce Scheduling 2.4 Multiperiod Problems 2.5 Modeling Constraints 2.6 Network Flow

      8  3 Linear Programming Formulations 3.1 Changing Form 3.2 Linearization of Piecewise Linear Functions 3.3 Dynamic Programming

      9  4 Integer Programming Models 4.1 Quantitative Variables and Fixed Costs 4.2 Set Covering 4.3 Logical Constraints and Piecewise Linear Functions 4.4 Additional Applications 4.5 Traveling Salesperson and Cutting Stock Problems

      10  5 Iterative Search Algorithms 5.1 Iterative Search and Constructive Algorithms 5.2 Improving Directions and Optimality 5.3 Computational Complexity and Correctness

      11  6 Convexity 6.1 Convex Sets 6.2 Convex and Concave Functions

      12  7 Geometry and Algebra of LPs 7.1 Extreme Points and Basic Feasible Solutions 7.2 Optimality of Extreme Points 7.3 Linear Programs in Canonical Form 7.4 Optimality Conditions 7.5 Optimality for General Polyhedra

      13  8 Duality Theory 8.1 Dual of a Linear Program 8.2 Duality Theorems 8.3 Complementary Slackness 8.4 Lagrangian Duality 8.5 Farkas' Lemma and Optimality

      14  9 Simplex Method 9.1 Simplex Method From a Known Feasible Solution 9.2 Degeneracy and Correctness 9.3 Finding an Initial Feasible Solution 9.4 Computational Strategies and Speed

      15  10 Sensitivity Analysis 10.1 Graphical Sensitivity Analysis 10.2 Shadow Prices and Reduced Costs 10.3 Economic Interpretation of the Dual

      16  11 Algorithmic Applications of Duality 11.1 Dual Simplex Method 11.2 Network Simplex Method 11.3 Primal‐Dual Interior Point Method

      17  12 Integer Programming Theory 12.1 Linear Programming Relaxations 12.2 Strong Formulations 12.3 Unimodular Matrices

      18  13 Integer Programming Algorithms 13.1 Branch and Bound Methods 13.2 Cutting Plane Methods

      19  14 Convex Programming: Optimality Conditions Скачать книгу