FS 15 | Standard|OverviewConvexity plays a central role in the design and analysis of modern and highly successful algorithms for solving real-world optimization problems. The lecture (in English) on convex optimization will treat in a balanced manner theory (convex analysis, optimality conditions) and algorithms for convex optimization. The lecture will follow mostly albeit loosely the textbook by S. Boyd and L. Vandenberghe, Convex Optimization, made available on the net (download) ReferencesA. Barvinok, A Course in Convexity. American Mathematical Society, 2003.
A. Ben-Tal and A. Nemirovski,
Lectures on Modern Convex Optimization - Analysis, Algorithms, and
Engineering Applications, MPS-SIAM Series on Optimization, MPS-SIAM.
D. P. Bertsekas, A. Nedic and A. E. Ozdaglar, Convex Analysis and Optimization, Athena Scientific, 2003. D. Bertsimas and J. N. Tsitsiklis, Introduction to Linear Optimization, Athena Scientific, 1997. S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. SIAM, 1994. E. de Klerk, Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications, Book Series: APPLIED OPTIMIZATION, Vol. 65. Kluwer Academic Publishers. Y.
Nesterov, Introductory Lectures on Convex Optimization: A Basic Course,
Book Series: APPLIED OPTIMIZATION, Vol. 87. Kluwer Academic Publishers.
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
J. Renegar, A Mathematical View of Interior-Point Methods in Convex Optimization, MPS-SIAM Series on Optimization.
R.T. Rockafellar, Convex Analysis, Princeton University Press, 1997.
H. Wolkowicz, R. Saigal and L. Vandenberghe, Handbook of Semidefinite
Programming: Theory, Algorithms, and Applications, Kluwer Academic
Publishers.
A. Nemirovski and D. Yudin, Problem Complexity and Method Efficiency in Optimization, John Wiley, 1983.
Y. Nesterov and A. Nemirovski, Interior Point Polynomial Algorithms in
Convex Programming, Studies in Applied Mathematics Vol. 13, SIAM, 1993.
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