Primal-Dual Interior-Point Methods for Self-Scaled Cones

Authors:
Yu. E. Nesterov;M. J. Todd
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
1998

Citing 0
Cited 25

Primal-Dual Path-Following Algorithms for Determinant Maximization Problems With Linear Matrix Inequalities

Computational Optimization and Applications
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming

STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On a commutative class of search directions for linear programming over symmetric cones

Journal of Optimization Theory and Applications
Nonnegative minimum biased quadratic estimation in mixed linear models

Journal of Multivariate Analysis
Computational Experience with Ill-Posed Problems in Semidefinite Programming

Computational Optimization and Applications
SDPARA: semiDefinite programming algorithm paRAllel version

Parallel Computing
Review of "A mathematical view of interior-point methods in convex optimization", by James Renegar, SIAM, Philadelphia, PA

Mathematics of Computation
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming

Journal of Computer and System Sciences - STOC 2001
Approximate minimum enclosing balls in high dimensions using core-sets

Journal of Experimental Algorithmics (JEA)
A conversion of an SDP having free variables into the standard form SDP

Computational Optimization and Applications
A primal--dual symmetric relaxation for homogeneous conic systems

Journal of Complexity
Parabolic target space and primal-dual interior-point methods

Discrete Applied Mathematics
Complexity of the primal-dual path-following algorithms for the weighted determinant maximization problems with linear matrix inequalities in the narrow neighbourhood

Optimization Methods & Software
Numerical experiments with universal barrier functions for cones of Chebyshev systems

Computational Optimization and Applications
Nonlinear and linear broadcasting with QoS requirements: tractable approaches for bounded channel uncertainties

IEEE Transactions on Signal Processing
A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO

Numerical Algorithms
A New Class of Large Neighborhood Path-Following Interior Point Algorithms for Semidefinite Optimization with $O(\sqrt{n}\log\frac{\mathrm{Tr}(X^0S^0)}{\epsilon})$ Iteration Complexity

SIAM Journal on Optimization
Superlinear Convergence of an Infeasible Predictor-Corrector Path-Following Interior Point Algorithm for a Semidefinite Linear Complementarity Problem Using the Helmberg-Kojima-Monteiro Direction

SIAM Journal on Optimization
A large-update primal-dual interior-point method for second-order cone programming

ISNN'10 Proceedings of the 7th international conference on Advances in Neural Networks - Volume Part I
Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step

Numerical Algorithms
Algorithm 925: Parallel Solver for Semidefinite Programming Problem having Sparse Schur Complement Matrix

ACM Transactions on Mathematical Software (TOMS)
High-performance general solver for extremely large-scale semidefinite programming problems

SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

International Journal of Fuzzy System Applications
A homotopy method for nonlinear semidefinite programming

Computational Optimization and Applications
A new O(nL) -iteration predictor-corrector algorithm with wide neighborhood for semidefinite programming

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see Yu. E. Nesterov and M. J. Todd, Math. Oper. Res., 22 (1997), pp. 1--42). The class of problems under consideration includes linear programming, semidefinite programming, and convex quadratically constrained, quadratic programming problems. For such problems we introduce a new definition of affine-scaling and centering directions. We present efficiency estimates for several symmetric primal-dual methods that can loosely be classified as path-following methods. Because of the special properties of these cones and barriers, two of our algorithms can take steps that typically go a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier.