Solving Optimization Problems with MATLAB 1st edition by Dingyü Xue – Ebook PDF Instant Download/Delivery: 3110663694 , 9783110663693
Full download Solving Optimization Problems with MATLAB 1st edition after payment
Product details:
ISBN 10: 3110663694
ISBN 13: 9783110663693
Author: Dingyü Xue
This book focuses on solving optimization problems with MATLAB. Descriptions and solutions of nonlinear equations of any form are studied first. Focuses are made on the solutions of various types of optimization problems, including unconstrained and constrained optimizations, mixed integer, multiobjective and dynamic programming problems. Comparative studies and conclusions on intelligent global solvers are also provided.
Solving Optimization Problems with MATLAB 1st Table of contents:
1 An introduction to equations and optimization problems
1.1 Equations and their solutions
1.2 Origins and development of optimization problems
1.3 Structure of the book
1.4 Exercises
2 Solutions of algebraic equations
2.1 Solutions of polynomial equations
2.1.1 Polynomial equations of degrees 1 and 2
2.1.2 Analytical solutions of cubic equations
2.1.3 Analytical solutions of quartic equation
2.1.4 Higher-degree equations and Abel–Ruffini theorem
2.2 Graphical methods for nonlinear equations
2.2.1 Smooth graphics for implicit functions
2.2.2 Univariate equations
2.2.3 Equations with two unknowns
2.2.4 Isolated equation solutions
2.3 Numerical solutions of algebraic equations
2.3.1 Newton–Raphson iterative algorithm
2.3.2 Direct solution methods with MATLAB
2.3.3 Accuracy specifications
2.3.4 Complex domain solutions
2.4 Accurate solutions of simultaneous equations
2.4.1 Analytical solutions of low-degree polynomial equations
2.4.2 Quasianalytical solutions of polynomial-type equations
2.4.3 Quasianalytical solutions of polynomial matrix equations
2.4.4 Quasianalytical solutions of nonlinear equations
2.5 Nonlinear matrix equations with multiple solutions
2.5.1 An equation solution idea and its implementation
2.5.2 Pseudopolynomial equations
2.5.3 A quasianalytical solver
2.6 Underdetermined algebraic equations
2.7 Exercises
3 Unconstrained optimization problems
3.1 Introduction to unconstrained optimization problems
3.1.1 The mathematical model of unconstrained optimization problems
3.1.2 Analytical solutions of unconstrained minimization problems
3.1.3 Graphical solutions
3.1.4 Local and global optimum solutions
3.1.5 MATLAB implementation of optimization algorithms
3.2 Direct solutions of unconstrained optimization problem with MATLAB
3.2.1 Direct solution methods
3.2.2 Control options in optimization
3.2.3 Additional parameters
3.2.4 Intermediate solution process
3.2.5 Structured variable description of optimization problems
3.2.6 Gradient information
3.2.7 Optimization solutions from scattered data
3.2.8 Parallel computation in optimization problems
3.3 Towards global optimum solutions
3.4 Optimization with decision variable bounds
3.4.1 Univariate optimization problem
3.4.2 Multivariate optimization problems
3.4.3 Global optimum solutions
3.5 Application examples of optimization problems
3.5.1 Solutions of linear regression problems
3.5.2 Least-squares curve fitting
3.5.3 Shooting method in boundary value differential equations
3.5.4 Converting algebraic equations into optimization problems
3.6 Exercises
4 Linear and quadratic programming
4.1 An introduction to linear programming
4.1.1 Mathematical model of linear programming problems
4.1.2 Graphical solutions of linear programming problems
4.1.3 Introduction to the simplex method
4.2 Direct solutions of linear programming problems
4.2.1 A linear programming problem solver
4.2.2 Linear programming problems with multiple decision vectors
4.2.3 Linear programming with double subscripts
4.2.4 Transportation problem
4.3 Problem-based description and solution of linear programming problems
4.3.1 MPS file for linear programming problems
4.3.2 Problem-based description of linear programming problems
4.3.3 Conversions in linear programming problems
4.4 Quadratic programming
4.4.1 Mathematical quadratic programming models
4.4.2 Direct solutions of quadratic programming problems
4.4.3 Problem-based quadratic programming problem description
4.4.4 Quadratic programming problem with double subscripts
4.5 Linear matrix inequalities
4.5.1 Description of linear matrix inequality problems
4.5.2 Lyapunov inequalities
4.5.3 Classifications of LMI problems
4.5.4 MATLAB solutions of LMI problems
4.5.5 Optimization solutions with YALMIP toolbox
4.5.6 Trials on nonconvex problems
4.5.7 Problems with quadratic constraints
4.6 Exercises
5 Nonlinear programming
5.1 Introduction to nonlinear programming
5.1.1 Mathematical models of nonlinear programming problems
5.1.2 Feasible regions and graphical methods
5.1.3 Examples of numerical methods
5.2 Direct solutions of nonlinear programming problems
5.2.1 Direct solution using MATLAB
5.2.2 Handling of earlier termination phenomenon
5.2.3 Gradient information
5.2.4 Solving problems with multiple decision vectors
5.2.5 Complicated nonlinear programming problems
5.3 Trials with global nonlinear programming solver
5.3.1 Trials on global optimum solutions
5.3.2 Nonconvex quadratic programming problems
5.3.3 Concave-cost transportation problem
5.3.4 Testing of the global optimum problem solver
5.3.5 Handling piecewise objective functions
5.4 Bilevel programming problems
5.4.1 Bilevel linear programming problems
5.4.2 Bilevel quadratic programming problem
5.4.3 Bilevel program solutions with YALMIP Toolbox
5.5 Nonlinear programming applications
5.5.1 Maximum inner polygon inside a circle
5.5.2 Semiinfinite programming problems
5.5.3 Pooling and blending problem
5.5.4 Optimization design of heat exchange network
5.5.5 Solving nonlinear equations with optimization techniques
5.6 Exercises
6 Mixed integer programming
6.1 Introduction to integer programming
6.1.1 Integer and mixed-integer programming problems
6.1.2 Computational complexity of integer programming problems
6.2 Enumeration methods for integer programming
6.2.1 An introduction to the enumeration method
6.2.2 Discrete programming
6.2.3 0−1 programming
6.2.4 Trials on mixed-integer programming problems
6.3 Solutions of mixed-integer programming problems
6.3.1 Mixed-integer linear programming
6.3.2 Integer programming with YALMIP Toolbox
6.3.3 Mixed-integer nonlinear programming
6.3.4 A class of discrete programming problems
6.3.5 Solutions of ordinary discrete programming problems
6.4 Mixed 0−1 programming problems
6.4.1 0–1 linear programming problems
6.4.2 0–1 nonlinear programming problems
6.5 Mixed-integer programming applications
6.5.1 Optimal material usage
6.5.2 Assignment problem
6.5.3 Traveling salesman problem
6.5.4 Knapsack problems
6.5.5 Sudoku problems
6.6 Exercises
7 Multiobjective programming
7.1 Introduction to multiobjective programming
7.1.1 Background introduction
7.1.2 Mathematical model of multiobjective programming
7.1.3 Graphical solution of multiobjective programming problems
7.2 Multiobjective programming conversions and solutions
7.2.1 Least-squares solutions of multiobjective programming problems
7.2.2 Linear weighting conversions
7.2.3 Best compromise solution of linear programs
7.2.4 Least-squares linear programming
7.3 Pareto optimal solutions
7.3.1 Nonuniqueness of multiobjective programming
7.3.2 Dominant solutions and Pareto frontiers
7.3.3 Computations of Pareto frontier
7.4 Minimax problems
7.5 Exercises
8 Dynamic programming and shortest paths
8.1 An introduction to dynamic programming
8.1.1 Concept and mathematical models in dynamic programming
8.1.2 Dynamic programming solutions of linear programming problems
8.2 Shortest path problems in oriented graphs
8.2.1 Examples of oriented graphs
8.2.2 Manual solutions of shortest path problem
8.2.3 Solution with dynamic programming formulation
8.2.4 Matrix representation of graphs
8.2.5 Finding the shortest path
8.2.6 Dijkstra algorithm implementation
8.3 Optimal paths for undigraphs
8.3.1 Matrix description
8.3.2 Route planning for cities with absolute coordinates
8.4 Exercises
9 Introduction to intelligent optimization methods
9.1 Intelligent optimization algorithms
9.1.1 Genetic algorithms
9.1.2 Particle swarm optimization methods
9.2 MATLAB Global Optimization Toolbox
9.3 Examples and comparative studies of intelligent optimization methods
9.3.1 Unconstrained optimization problems
9.3.2 Constrained optimization problems
9.3.3 Mixed-integer programming
9.3.4 Discrete programming problems with the genetic algorithm
9.4 Exercises
Bibliography
Subject Index
Sachregister
People also search for Solving Optimization Problems with MATLAB 1st :
how to solve optimization problems
solve optimization matlab
matlab optimization problem
matlab optimization examples
matlab optimization solve
Tags: Dingyü Xue, Solving Optimization, Problems with MATLAB
Reviews
There are no reviews yet.