The field of semidefinite programming (SDP) or semidefinite optimization (SDO) deals with optimization problems over symmetric positive semidefinite matrix variables with linear cost function and linear constraints. Popular special cases are linear programming and convex quadratic programming with convex quadratic constraints.
Semidefinite Programming
This entry contributed by Suliman Al-Homidan
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References
Boyd, S.; El Ghaoui, L.; Feron, E.; and Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.de Klerk, E. Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications. Dordrecht, Netherlands: Kluwer, 2002.El Ghaoui, L. and Niculescu, S.-I. (Eds.). Advances in Linear Matrix Inequality Methods in Control. Philadelphia, PA: SIAM, 2000.Helmberg, C. "Semidefinite Programming for Combinatorial Optimization." Habilitationsschrift, TU Berlin, January 2000. ZIB-Report ZR-00-34, Konrad-Zuse-Zentrum Berlin, October 2000.Laurent, M. and Rendl, F. "Semidefinite Programming and Integer Programming." Report PNA-R0210, CWI, Amsterdam, April 2002.Nesterov, Y. and Nemirovskii, A. Interior-Point Polynomial Algorithms in Convex Programming. Philadelphia, PA: SIAM, 1993.Pardalos, P. M. and Wolkowicz, H. (Eds.). "Topics in Semidefinite and Interior Point Methods." Providence, RI: Amer. Math. Soc., 1998.Todd, M. "Semidefinite Optimization." Acta Numerica 10, 515-560, 2001.Vandenberghe, L. and Boyd, S. "Semidefinite Programming." SIAM Rev. 38, 49-95, Mar. 1996.Wolkowicz, H.; Saigal, R.; and Vandenberghe, L. (Eds.). Handbook on Semidefinite Programming: Theory, Algorithms, and Applications. Dordrecht, Netherlands: Kluwer, 2000.Referenced on Wolfram|Alpha
Semidefinite ProgrammingCite this as:
Al-Homidan, Suliman. "Semidefinite Programming." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SemidefiniteProgramming.html