Geodesic
A method for semidefinite quasiconvex maximization problem
The Bulletin of Irkutsk State University. Series Mathematics, Tome 18 (2016), pp. 110-121 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce so-called semidefinite quasiconvex maximization problem. We derive new global optimality conditions by generalizing [9]. Using these conditions, we construct an algorithm which generates a sequence of local maximizers that converges to a global solution. Also, new applications of semidefinite quasiconvex maximization are given. Subproblems of the proposed algorithm are semidefinite linear programming.
Keywords: semidefinite linear programming, global optimality conditions, semidefinite quasiconvex maximization, algorithm, approximation set. 
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R. Enkhbat; M. Bellalij; K. Jbilou; T. Bayartugs. A method for semidefinite quasiconvex maximization problem. The Bulletin of Irkutsk State University. Series Mathematics, Tome 18 (2016), pp. 110-121. http://geodesic.mathdoc.fr/item/IIGUM_2016_18_a7/

[1] Arslan G., Demirkol M. F., Song Y., “Equilibrium efficiency improvement in MIMO interference systems: a desentralized stream control apprioch”, IEEE Transaction on Wireless Communications, 6:8, August (2007), 2984–2993 | DOI

[2] Bouhamidi A., Enkhbat R., Jbilou K., “Semidefinite Concave Programming”, Journal of Mongolian Mathematical Society, 16 (2012), 37–46 | MR | Zbl

[3] Balakrishnan A. V., Introduction to Optimization Theory in a Hilbert Space, Springer-Verlag, 1970 | MR

[4] Enkhbat R., Quasiconvex Programming and its Applications, Lambert Publisher, Germany, 2009

[5] Enkhbat R., Bayartugs T., “Quasiconvex Semidefinite Minimization Problem”, Journal of Optimization: Hindawi Publishing Corporation, 201 (2013), 346131, 6 pp.

[6] Enkhbat R., Bayartugs T., “Semidefinite Quasiconcave programming”, International Journal of Pure and Applied Mathematics, 87:4 (2013), 547–557 | DOI | MR

[7] Pardalos P. M., Wolkowicz H. (eds.), Topics in Semidefinite and Interior Point Methods, Fields Institute Communications 18, AMS, Providence, Rhode Island, 1998 | MR

[8] Rockafellar R. T., Convex Analysis, Princeton University Press, 1970 | MR | Zbl

[9] Strekalovsky A. S., “Global Optimality Conditions for Nonconvex Optimization”, Journal of Global Optimization, 12 (1998), 415–434 | DOI | MR | Zbl

[10] Strekalovsky A. S., Enkhbat R., Global Maximum of Convex Functions on an Arbitrary Set, Dep. in VINITI No 1063, Irkutsk, 1990, 27 pp.

[11] Malick J., Povh J., Rendl F., Wiegele A., Regularization methods for semidefinite programming, September 1, 2008 | MR

[12] Sigen Ye, Blum R. S., “Optimized signaling for MIMO interference systems with feedback”, IEEE Transactions on Signal Processing, 51:11 (2003), 2839–2848 | DOI

[13] Vandenberghe L., Boyd S., “Semidefinite programming”, SIAM Rev., 38 (1996), 49–95 | DOI | MR | Zbl

[14] Zhang Y., “On extending some primal-dual interior point algorithms from linear programming to semidefinite programming”, SIAM Journal on Optimization, 8:2 (1998), 365–386 | DOI | MR | Zbl

[15] Zhang L., Zhang Y., Liang Y. C., Xin Y., Poor H. V., “On the Gaussian MIMO BC-MAC duality with multiple transmit covarianca constraints”, IEEE Transactions on Information Theory, 58:4, april (2012) | MR

[16] Tzu-Chen Liang, Ta-Chung Wang, Yinyu Ye, A Gradient Search Method to Round the Semidefinite Programming Relaxation Solution for Ad Hoc Wireless Sensor Network Localization, TECHNICAL REPORT SOL 2004-2, December, 2004

[17] Wolkowicz H., Saigal R., Vandenberghe L., Handbook of Semidefinite Programming, Kluwer, 2000 | MR

[18] Jansen K., Rolim J., Sudan M., Linear Semidefinite Programming and Randomization Methods for Combinatorial Optimization Problems, Dagstuhl Seminar No 00041, Report No 263, 2012