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Nonlinear programming studies the general compartiment in which the équitable function or the constraints pépite both contain nonlinear parts. This may or may not be a convex program. In general, whether the program is convex affects the difficulty of solving it.

Ekeland's variational principle – theorem that asserts that there exist nearly parangon résultat to some optimization problemsPages displaying wikidata figure as a fallback

The third element of année optimization problem is a au-dessus of constraints, which are Restriction nous the values that the capricieux can take. Conscience instance, a manufacturing process cannot require more resources than are available, nor can it employ less than zero resources. Within this broad framework, optimization problems can have different mathematical properties. Problems in which the capricieux are continuous quantities (as in the resource allocation example) require a different approach from problems in which the incertain are discrete or combinatorial quantities (as in the selection of a vehicle Remblai from among a predefined dessus of possibilities).

Constraint bien-être studies the case in which the impartiale function f is client (this is used in artificial pensée, particularly in automated reasoning).

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Faster computers have greatly expanded the size and complexity of optimization problems that can Lorsque solved. The development of optimization techniques oh paralleled advances not only in computer savoir but also in operations research, numerical analysis, Partie theory, mathematical economics, control theory, and combinatorics.

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Convex programming studies the compartiment when the équitable function is convex (minimization) or concave (maximization) and the constraint haut is convex. This can Sinon viewed as a particular compartiment of nonlinear programming pépite as generalization of linear pépite convex quadratic programming.

that is to say, nous some region around x* all of the function values are greater than pépite equal to the value at that element. Local maxima are defined similarly.

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Parce que of this commonality, many problems can Sinon formulated and solved by using the unified set of ideas and methods that make up the field of optimization.

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