Arabic Chrestomathy in Hebrew Characters by Hartwig Hirschfeld

By Hartwig Hirschfeld

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Soyster. Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21(5), 1154– 1157 (1973). 26. L. El Ghaoui and H. Lebret. Robust solutions to least-squares problems with uncertain data. SIAM J. Matrix Anal. , 18(4), 1035– 1064 (1997). 27. A. Ben-Tal and A. Nemirovski. Robust convex optimization. Mathematics of Operations Research, 23(4), 769– 805 (1998). 28. A. Ben-Tal, L. El Ghaoui, and A. Nemirovski. Robustness. In Handbook on Semidefinite Programming, Chapter 6, pp.

Wu and S. P. Boyd. SDPSOL: A parser/solver for semidefinite programs with matrix structure. In L. -I. Niculescu, Eds. Advances in Linear Matrix Inequality Methods in Control, Chapter 4, pp. 79– 91. SIAM, Philadelphia, 2000. 40. L. Vandenberghe, S. P. -P. Wu. Determinant maximization with linear matrix inequality constraints. SIAM J. Matrix Anal. , 19(2), 499 – 533 (1998). 41. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, Vol. 15, Studies in Applied Mathematics, SIAM, Philadelphia, June 1994.

23 –24], E i # E 0 for i ¼ 1, . . , p if and only if there exists non-negative scalars t1 , . . , tp such that T0 (x) À ti Ti (x) 0, i ¼ 1, . . , p, or equivalently, such that 2 F0 4 gT0 0 g0 À1 g0 3 2 0 Fi gT0 5 À ti 4 gTi ÀF0 0 gi hi 0 3 0 05 0 0, for i ¼ 1, . . , p: We can find the MVE containing the union of ellipsoids E 1 , . . , E p by solving the matrix completion problem: minimize log det F0À1 F0 . 0, t1 ! 0, . . , tp ! 0, 3 2 g0 0 Fi gi 6 T T7 À1 g 0 5 À t i 4 gi hi subject to 2 F0 6 T 4 g0 0 g0 ÀF0 0 0 3 0 7 05 0, 0 for i ¼ 1, .

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