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.

Read more about this topic:  Optimization Problem

Famous quotes containing the words continuous and/or problem:

    “We read poetry because the poets, like ourselves, have been haunted by the inescapable tyranny of time and death; have suffered the pain of loss, and the more wearing, continuous pain of frustration and failure; and have had moods of unlooked-for release and peace. They have known and watched in themselves and others.”
    —Elizabeth Drew (1887–1965)

    “Hypocrisy is the essence of snobbery, but all snobbery is about the problem of belonging.”
    —Alexander Theroux (b. 1940)