An Interior-Point Method for Semidefinite Programming

We propose a new interior-point-based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices....

[1]  F. Hadlock,et al.  Finding a Maximum Cut of a Planar Graph in Polynomial Time , 1975, SIAM J. Comput..

[2]  P. Wolfe,et al.  The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices , 1975 .

[3]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[4]  H. Wolkowicz,et al.  Some applications of optimization in matrix theory , 1981 .

[5]  F. Barahona.  The max-cut problem on graphs not contractible to K5 , 1983 .

[6]  Ravi B. Boppana,et al.  Eigenvalues and graph bisection: An average-case analysis , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[7]  M. Overton.  On minimizing the maximum eigenvalue of a symmetric matrix , 1988 .

[8]  Jochem Zowe,et al.  A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results , 1992, SIAM J. Optim..

[9]  Michael L. Overton,et al.  Large-Scale Optimization of Eigenvalues , 1990, SIAM J. Optim..

[10]  Monique Laurent,et al.  The Metric Polytope , 1992, Conference on Integer Programming and Combinatorial Optimization.

[11]  F. Jarre.  An interior-point method for minimizing the maximum eigenvalue of a linear combination of matrices , 1993 .

[12]  John M. Mulvey,et al.  Higher-Order Predictor-Corrector Interior Point Methods with Application to Quadratic Objectives , 1993, SIAM J. Optim..

[13]  Robert J. Vanderbei,et al.  Symmetric indefinite systems for interior point methods , 1993, Math. Program..

[14]  Charles Delorme,et al.  Laplacian eigenvalues and the maximum cut problem , 1993, Math. Program..

[15]  K. Anstreicher,et al.  On the convergence of an infeasible primal-dual interior-point method for convex programming , 1994 .

[16]  David P. Williamson,et al.  .879-approximation algorithms for MAX CUT and MAX 2SAT , 1994, STOC '94.

[17]  J. Vial.  Computational experience with a primal-dual interior-point method for smooth convex programming , 1994 .

[18]  Franz Rendl,et al.  A computational study of graph partitioning , 1994, Math. Program..

[19]  M. Overton,et al.  Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Nu , 1994 .

[20]  C. Helmberg.  An Interior Point Method for Semidefinite Programming and Max-Cut Bounds , 1994 .

[21]  Stephen P. Boyd,et al.  A primal—dual potential reduction method for problems involving matrix inequalities , 1995, Math. Program..

[22]  Shinji Hara,et al.  Interior Point Methods for the Monotone Linear Complementarity Problem in Symmetric Matrices , 1995 .

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

[24]  R. Vanderbei,et al.  Max-min eigenvalue problems, primal-dual Interior point algorithms, and Trust region subproblemst , 1995 .

[25]  Franz Rendl,et al.  Nonpolyhedral Relaxations of Graph-Bisection Problems , 1995, SIAM J. Optim..

[26]  F. Jarre.  Interior-point methods via self-concordance or relative lipschitz condition , 1995 .

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

[28]  Siam J. CoMPtrr,et al.  FINDING A MAXIMUM CUT OF A PLANAR GRAPH IN POLYNOMIAL TIME * , 2022 .