Optimization Problem - Continuous Optimization Problem

Continuous Optimization Problem

The standard form of a (continuous) optimization problem is

\begin{align} &\underset{x}{\operatorname{minimize}}& & f(x) \\ &\operatorname{subject\;to} & &g_i(x) \leq 0, \quad i = 1,\dots,m \\ &&&h_i(x) = 0, \quad i = 1, \dots,p \end{align}

where

  • is the objective function to be minimized over the variable ,
  • are called inequality constraints, and
  • are called equality constraints.

By convention, the standard form defines a minimization problem. A maximization problem can be treated by negating the objective function.

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