Linear and Convex Optimization A Mathematical Approach 1st Edition by Michael Veatch 9781119664055 1119664055

Linear and Convex Optimization A Mathematical Approach 1st Edition by Michael Veatch – Ebook PDF Instant Download/Delivery: 9781119664055, 1119664055

Full download Linear and Convex Optimization A Mathematical Approach 1st Edition after payment

Product details:

• ISBN 10:1119664055 

• ISBN 13:9781119664055

• Author:Michael Veatch 

Linear and Convex Optimization
A Mathematical Approach
Discover the practical impacts of current methods of optimization with this approachable, one-stop resource

Linear and Convex Optimization: A Mathematical Approach delivers a concise and unified treatment of optimization with a focus on developing insights in problem structure, modeling, and algorithms. Convex optimization problems are covered in detail because of their many applications and the fast algorithms that have been developed to solve them. 

Experienced researcher and undergraduate teacher Mike Veatch presents the main algorithms used in linear, integer, and convex optimization in a mathematical style with an emphasis on what makes a class of problems practically solvable and developing insight into algorithms geometrically. Principles of algorithm design and the speed of algorithms are discussed in detail, requiring no background in algorithms.

The book offers a breadth of recent applications to demonstrate the many areas in which optimization is successfully and frequently used, while the process of formulating optimization problems is addressed throughout. 

Linear and Convex Optimization contains a wide variety of features, including:

Coverage of current methods in optimization in a style and level that remains appealing and accessible for mathematically trained undergraduates
Enhanced insights into a few algorithms, instead of presenting many algorithms in cursory fashion
An emphasis on the formulation of large, data-driven optimization problems
Inclusion of linear, integer, and convex optimization, covering many practically solvable problems using algorithms that share many of the same concepts
Presentation of a broad range of applications to fields like online marketing, disaster response, humanitarian development, public sector planning, health delivery, manufacturing, and supply chain management
Ideal for upper level undergraduate mathematics majors with an interest in practical applications of mathematics, this book will also appeal to business, economics, computer science, and operations research majors with at least two years of mathematics training.

Linear and Convex Optimization A Mathematical Approach 1st Table of contents:

 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
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
3 Linear Programming Formulations
3.1 Changing Form
3.2 Linearization of Piecewise Linear Functions
3.3 Dynamic Programming
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
5 Iterative Search Algorithms
5.1 Iterative Search and Constructive Algorithms
5.2 Improving Directions and Optimality
5.3 Computational Complexity and Correctness
6 Convexity
6.1 Convex Sets
6.2 Convex and Concave Functions
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
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
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
10 Sensitivity Analysis
10.1 Graphical Sensitivity Analysis
10.2 Shadow Prices and Reduced Costs
10.3 Economic Interpretation of the Dual
11 Algorithmic Applications of Duality
11.1 Dual Simplex Method
11.2 Network Simplex Method
11.3 Primal‐Dual Interior Point Method
12 Integer Programming Theory
12.1 Linear Programming Relaxations
12.2 Strong Formulations
12.3 Unimodular Matrices
13 Integer Programming Algorithms
13.1 Branch and Bound Methods
13.2 Cutting Plane Methods
14 Convex Programming: Optimality Conditions
14.1 KKT Optimality Conditions
14.2 Lagrangian Duality
15 Convex Programming: Algorithms
15.1 Convex Optimization Models
15.2 Separable Programs
15.3 Unconstrained Optimization
15.4 Quadratic Programming
15.5 Primal‐dual Interior Point Method
A Linear Algebra and Calculus Review
A.1 Sets and Other Notation
A.2 Matrix and Vector Notation
A.3 Matrix Operations
A.4 Matrix Inverses
A.5 Systems of Linear Equations
A.6 Linear Independence and Rank
A.7 Quadratic Forms and Eigenvalues
A.8 Derivatives and Convexity
Bibliography
Index
End User License Agreement

People also search for Linear and Convex Optimization A Mathematical Approach 1st:

linear and convex optimization
    
linear and convex optimization a mathematical approach
    
linear and convex optimization a mathematical approach pdf
    
linear programming and convex optimization
    
what is convex optimization