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A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems
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Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices
TLDR
The aim of this paper is to establish a theoretical basis of interior-point methods with the use of Newton directions toward the central trajectory for the monotone SDLCP.
Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity
TLDR
Using a correlative sparsity pattern graph, sets of the supports for sums of squares polynomials that lead to efficient SOS and semidefinite program (SDP) relaxations are obtained.
A primal—dual infeasible-interior-point algorithm for linear programming
TLDR
A step length rule is proposed with which the algorithm takes large distinct step lengths in the primal and dual spaces and enjoys the global convergence.
A primal-dual interior point algorithm for linear programming
This chapter presents an algorithm that works simultaneously on primal and dual linear programming problems and generates a sequence of pairs of their interior feasible solutions. Along the sequence
Exploiting Sparsity in Semidefinite Programming via Matrix Completion I: General Framework
TLDR
A general method of exploiting the aggregate sparsity pattern over all data matrices to overcome a critical disadvantage of primal-dual interior-point methods for large scale semidefinite programs (SDPs).
A polynomial-time algorithm for a class of linear complementarity problems
TLDR
An algorithm is presented that solves the problem of finding n-dimensional vectors in O(n3L) arithmetic operations by tracing the path of centers by identifying the centers of centers of the feasible region.
Local convergence of predictor—corrector infeasible-interior-point algorithms for SDPs and SDLCPs
TLDR
An example of an SDP exhibits a substantial difficulty in proving the superlinear convergence of a direct extension of the Mizuno—Todd—Ye type predictor—corrector primal-dual interior-point method, and suggests that the authors need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory).
Algorithm 883: SparsePOP---A Sparse Semidefinite Programming Relaxation of Polynomial Optimization Problems
TLDR
The efficiency of SparsePOP to approximate optimal solutions of POPs is increased, and larger-scale POPs can be handled.
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