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:

    “There was a continuous movement now, from Zone Five to Zone Four. And from Zone Four to Zone Three, and from us, up the pass. There was a lightness, a freshness, and an enquiry and a remaking and an inspiration where there had been only stagnation. And closed frontiers. For this is how we all see it now.”
    —Doris Lessing (b. 1919)

    “Every reform was once a private opinion, and when it shall be a private opinion again, it will solve the problem of the age.”
    —Ralph Waldo Emerson (1803–1882)