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MP
2011
13 years 1 months ago
Implicit solution function of P0 and Z matrix linear complementarity constraints
Abstract. Using the least element solution of the P0 and Z matrix linear complementarity problem (LCP), we define an implicit solution function for linear complementarity constrai...
Xiaojun Chen, Shuhuang Xiang
MP
2011
13 years 1 months ago
An interior-point piecewise linear penalty method for nonlinear programming
We present an interior-point penalty method for nonlinear programming (NLP), where the merit function consists of a piecewise linear penalty function (PLPF) and an 2-penalty functi...
Lifeng Chen, Donald Goldfarb
MP
2011
13 years 1 months ago
Strong KKT conditions and weak sharp solutions in convex-composite optimization
Using variational analysis techniques, we study convex-composite optimization problems. In connection with such a problem, we introduce several new notions as variances of the clas...
Xi Yin Zheng, Kung Fu Ng
MP
2011
13 years 5 months ago
Smoothed analysis of condition numbers and complexity implications for linear programming
We perform a smoothed analysis of Renegar’s condition number for linear programming by analyzing the distribution of the distance to ill-posedness of a linear program subject to...
John Dunagan, Daniel A. Spielman, Shang-Hua Teng
MP
2011
13 years 5 months ago
A warm-start approach for large-scale stochastic linear programs
Marco Colombo, Jacek Gondzio, Andreas Grothey
MP
2011
13 years 5 months ago
Statistical ranking and combinatorial Hodge theory
We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced — characteristics that are almost universal to modern datasets co...
Xiaoye Jiang, Lek-Heng Lim, Yuan Yao, Yinyu Ye
MP
2011
13 years 5 months ago
A first-order interior-point method for linearly constrained smooth optimization
Abstract: We propose a first-order interior-point method for linearly constrained smooth optimization that unifies and extends first-order affine-scaling method and replicator d...
Paul Tseng, Immanuel M. Bomze, Werner Schachinger
MP
2011
13 years 5 months ago
Null space conditions and thresholds for rank minimization
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in machine learning, control theory, and discrete geometry. This c...
Benjamin Recht, Weiyu Xu, Babak Hassibi