Convex optimization: Difference between revisions

Revision as of 08:01, 10 December 2023

Revision as of 08:05, 10 December 2023

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[[File:Hierarchy compact convex.png|thumb|A hierarchy of convex optimization problems. (LP: linear program, QP: quadratic program, SOCP second-order cone program, SDP: semidefinite program, CP: cone program.)]]

*[[Linear programming]] problems are problems in which the objective and constraint functions are all linear. These are the simplest case of convex programs, and have specialized, efficient algorithms.

* Convex [[quadratic programming|quadratic minimization]] with linear constraints are the next-simplest.

*[[Second order cone programming]] are more general.

*[[Semidefinite programming]] are more general.

*[[Conic optimization]] are even more general - see figure to the right,

Other special cases include;

*[[Least squares]]

*[[Linear programming]]

* Convex [[quadratic programming|quadratic minimization]] with linear constraints

*[[Quadratically constrained quadratic programming|Quadratic minimization with convex quadratic constraints]]

*[[Conic optimization]]

*[[Geometric programming]]

*[[Entropy maximization]] with appropriate constraints.

*[[Second order cone programming]]

*[[Semidefinite programming]]

*[[Entropy maximization]] with appropriate constraints

==Properties==

The following are useful properties of convex optimization problems:<ref name="rockafellar93">{{cite journal | author = Rockafellar, R. Tyrrell | title = Lagrange multipliers and optimality | journal = SIAM Review | volume = 35 | issue = 2 | year = 1993 | pages = 183–238 |url = http://web.williams.edu/Mathematics/sjmiller/public_html/105Sp10/handouts/Rockafellar_LagrangeMultAndOptimality.pdf | doi=10.1137/1035044| citeseerx = 10.1.1.161.7209}}</ref><ref name="bv4"/>