## Introduction to Mathematical Optimization: From Linear Programming to MetaheuristicsThis book strives to provide a balanced coverage of efficient algorithms commonly used in solving mathematical optimization problems. It covers both the convectional algorithms and modern heuristic and metaheuristic methods. Topics include gradient-based algorithms such as Newton-Raphson method, steepest descent method, Hooke-Jeeves pattern search, Lagrange multipliers, linear programming, particle swarm optimization (PSO), simulated annealing (SA), and Tabu search. Multiobjective optimization including important concepts such as Pareto optimality and utility method is also described. Three Matlab and Octave programs so as to demonstrate how PSO and SA work are provided. An example of demonstrating how to modify these programs to solve multiobjective optimization problems using recursive method is discussed. |

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### Contents

Norms and Hessian Matrices | 11 |

RootFinding Algorithms | 25 |

System of Linear Equations | 35 |

Copyright | |

9 other sections not shown

### Common terms and phrases

accelerated PSO ants approximate basic feasible solution basic variables canonical form cities coefficients colony optimization computational constraints convergence convex current best diagonal efficient eigenvalues eigenvector equation evaluations example extreme points Figure Gauss-Seidel iteration genetic algorithms global best global minimum global optimal gradient Hooke-Jeeves pattern search implementation increase inequalities initial guess inverse Iteration Methods iteration procedure Lagrange multipliers linear programming linear system locations maximize maximum metaheuristic metaheuristic methods minimization multiobjective optimization Newton's method non-basic variables non-dominated non-negative non-zero nonlinear norms number of iterations objective function objective function f(x optimal solution optimization problems parameter Pareto front Pareto optimal particle swarm optimization pheromone concentration random recursive route shown in Fig simplex method simulated annealing solve spectral radius square matrix stationary condition steepest descent method step swap Tabu list Tabu search temperature test function tion travelling salesman problem triangular matrix update utility function vector weighted sum zero