How to advance in Structural Convex Optimization

In this paper we are trying to analyze the common features of the recent advances in Structural Convex Optimization: polynomial-time interior-point methods, smoothing technique, minimization in relative scale, and minimization of composite functions.

[1]  Michael H. Bowling,et al.  Particle Filtering for Dynamic Agent Modelling in Simplified Poker , 2007, AAAI.

[2]  Michael L. Overton,et al.  Second Derivatives for Optimizing Eigenvalues of Symmetric Matrices , 1995, SIAM J. Matrix Anal. Appl..

[3]  B. Stengel,et al.  Efficient Computation of Behavior Strategies , 1996 .

[4]  Tuomas Sandholm,et al.  Optimal Rhode Island Hold'em Poker , 2005, AAAI.

[5]  Franz Rendl,et al.  A Spectral Bundle Method for Semidefinite Programming , 1999, SIAM J. Optim..

[6]  Farid Alizadeh,et al.  Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization , 1995, SIAM J. Optim..

[7]  Arkadi Nemirovski,et al.  Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems , 2004, SIAM J. Optim..

[8]  Tuomas Sandholm,et al.  Finding equilibria in large sequential games of imperfect information , 2006, EC '06.

[9]  Y. Nesterov Gradient methods for minimizing composite objective function , 2007 .

[10]  G. M. Korpelevich The extragradient method for finding saddle points and other problems , 1976 .

[11]  M. J. D. Powell,et al.  Nonlinear Programming—Sequential Unconstrained Minimization Techniques , 1969 .

[12]  O. Nelles,et al.  An Introduction to Optimization , 1996, IEEE Antennas and Propagation Magazine.

[13]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[14]  Yurii Nesterov,et al.  Rounding of convex sets and efficient gradient methods for linear programming problems , 2004, Optim. Methods Softw..

[15]  John Darzentas,et al.  Problem Complexity and Method Efficiency in Optimization , 1983 .

[16]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[17]  Yurii Nesterov,et al.  Smooth minimization of non-smooth functions , 2005, Math. Program..

[18]  Yurii Nesterov,et al.  Excessive Gap Technique in Nonsmooth Convex Minimization , 2005, SIAM J. Optim..

[19]  Jonathan Schaeffer,et al.  The challenge of poker , 2002, Artif. Intell..

[20]  Alexandre d'Aspremont,et al.  First-Order Methods for Sparse Covariance Selection , 2006, SIAM J. Matrix Anal. Appl..

[21]  François Oustry,et al.  A second-order bundle method to minimize the maximum eigenvalue function , 2000, Math. Program..

[22]  Stephen P. Boyd,et al.  The Fastest Mixing Markov Process on a Graph and a Connection to a Maximum Variance Unfolding Problem , 2006, SIAM Rev..

[23]  David P. Williamson,et al.  Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming , 1995, JACM.

[24]  R. Polyak Smooth optimization methods for minimax problems , 1988 .

[25]  Yurii Nesterov,et al.  Smoothing Technique and its Applications in Semidefinite Optimization , 2004, Math. Program..

[26]  Javier Peña,et al.  Gradient-Based Algorithms for Finding Nash Equilibria in Extensive Form Games , 2007, WINE.

[27]  Alexandre d'Aspremont,et al.  Model Selection Through Sparse Maximum Likelihood Estimation , 2007, ArXiv.

[28]  Yurii Nesterov,et al.  Introductory Lectures on Convex Optimization - A Basic Course , 2014, Applied Optimization.

[29]  Javier Peña,et al.  Smoothing Techniques for Computing Nash Equilibria of Sequential Games , 2010, Math. Oper. Res..

[30]  Renato D. C. Monteiro,et al.  Large-scale semidefinite programming via a saddle point Mirror-Prox algorithm , 2007, Math. Program..

[31]  Yurii Nesterov,et al.  Unconstrained Convex Minimization in Relative Scale , 2003, Math. Oper. Res..

[32]  Y. Nesterov A method for unconstrained convex minimization problem with the rate of convergence o(1/k^2) , 1983 .

[33]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[34]  Y. Nesterov Primal-Dual Subgradient Methods for Convex Problems , 2005 .

[35]  Kilian Q. Weinberger,et al.  Unsupervised Learning of Image Manifolds by Semidefinite Programming , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..