01 - Introduction

• Mathematical Program

  在数学的环境下 program 就是指优化问题：

  $$\min f(x) \;\; s.t. x \in S$$
  • $f(x)$: objective function
  • $x$: variable
  • $x \in S$: constrain

  Mathematical Programming = Mathematical Optimization

• Typical steps for solving mathematical optimization problem

  • Problem formulation (which is an art, time would be saved if problem is formulated properly)
    • define $f(x)$, $S$
  • Checking the existence of a solution
  • Solving the optimization problem, if a solution exists
    • Graphical method (suitable for functions of 1 or 2 variables)
    • Analytical method
    • Numerical method (iterative algorithm)
  • Solution analysis
  • Algorithm analysis

• Types of optimization problem

  • Constrained and unconstrained optimization
  • Continuous and discrete optimization

  • Stochastic and deterministic optimization

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• Types of optimization algorithm

  • Local optimization algorithm

  • Global optimization algorithm

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