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 is no such thing as a life of passion any more than a continuous earthquake, or an eternal fever. Besides, who would ever shave themselves in such a state?”
    —George Gordon Noel Byron (1788–1824)

    “The writer operates at a peculiar crossroads where time and place and eternity somehow meet. His problem is to find that location.”
    —Flannery O’Connor (1925–1964)