Quadratic programming: Difference between revisions

Revision as of 22:22, 10 November 2021

Revision as of 20:01, 13 December 2021

Line 10:

Given:

* a [[real number|real]]-valued, {{mvar|n}}-dimensional vector {{math|'''c'''}},

* an {{math|''n'' × ''n''}}-dimensional real [[symmetric matrix]] {{mvar|Q}},

* an {{math|''m'' × ''n''}}-dimensional real [[matrix (mathematics)|matrix]] {{mvar|A}}, and

* an {{mvar|m}}-dimensional real vector {{math|'''b'''}},

the objective of quadratic programming is to find an {{mvar|n}}-dimensional vector {{math|'''x'''}}, that will

Line 40:

===Generalizations===

When minimizing a function {{mvar|f}} in the neighborhood of some reference point {{math|''x''₀}}, {{mvar|Q}} is set to its [[Hessian matrix]] {{math|'''H'''(''f'' ('''x'''₀))}} and {{math|'''c'''}} is set to its [[gradient]] {{math|∇''f'' ('''x'''₀)}}. A related programming problem, [[quadratically constrained quadratic program]]ming, can be posed by adding quadratic constraints on the variables.

==Solution methods==