Semidefinite programming: Difference between revisions

Revision as of 06:13, 23 October 2023

Revision as of 02:37, 2 November 2023

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Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in [[operations research]] and [[combinatorial optimization]] can be modeled or approximated as semidefinite programming problems. In automatic control theory, SDPs are used in the context of [[linear matrix inequality|linear matrix inequalities]]. SDPs are in fact a special case of [[conic optimization|cone programming]] and can be efficiently solved by [[interior point methods]].

All [[linear programming|linear programs]] and (convex) [[quadratic programming|quadratic programs]] can be expressed as SDPs, and [[sum-of-squares optimization | via hierarchies of SDPs]] the solutions of polynomial optimization problems can be approximated. Semidefinite programming has been used in the [[optimization]] of complex systems. In recent years, some quantum query complexity problems have been formulated in terms of semidefinite programs.

== Motivation and definition ==

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{{Mathematical optimization software}}

{{Authority control}}

[[Category:Convex optimization]]