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:

    “If an irreducible distinction between theatre and cinema does exist, it may be this: Theatre is confined to a logical or continuous use of space. Cinema ... has access to an alogical or discontinuous use of space.”
    —Susan Sontag (b. 1933)

    “Involuntary mental hospitalization is like slavery. Refining the standards for commitment is like prettifying the slave plantations. The problem is not how to improve commitment, but how to abolish it.”
    —Thomas Szasz (b. 1920)