Matrix analysis
Perturbation bounds for matrix eigenvalues
Perturbation bounds for matrix eigenvalues
The molecule problem: determining conformation from pairwise distances
The molecule problem: determining conformation from pairwise distances
A new complexity result on minimization of a quadratic function with a sphere constraint
Recent advances in global optimization
A new lower bound via projection for the quadratic assignment problem
Mathematics of Operations Research
On adaptive-step primal-dual interior-point algorithms for linear programming
Mathematics of Operations Research
Trust Region Problems and Nonsymmetric Eigenvalue Perturbations
SIAM Journal on Matrix Analysis and Applications
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
The Euclidian Distance Matrix Completion Problem
SIAM Journal on Matrix Analysis and Applications
Convex relaxations of (0, 1)-quadratric programming
Mathematics of Operations Research
A semidefinite framework for trust region subproblems with applications to large scale minimization
Mathematical Programming: Series A and B
Semidefinite programming in combinatorial optimization
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Exploiting sparsity in primal-dual interior-point methods for semidefinite programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Cuts, matrix completions and graph rigidity
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
Self-scaled barriers and interior-point methods for convex programming
Mathematics of Operations Research
The symmetric eigenvalue problem
The symmetric eigenvalue problem
An Interior-Point Method for Approximate Positive Semidefinite Completions
Computational Optimization and Applications
Determinant Maximization with Linear Matrix Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
Approximate Semidefinite Matrices in a Linear Variety
SIAM Journal on Matrix Analysis and Applications
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Semidefinite programming and combinatorial optimization
HPOPT '96 Proceedings of the Stieltjes workshop on High performance optimization techniques
Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Strengthened semidefinite relaxations via a second lifting for the Max-Cut problem
Discrete Applied Mathematics
Optimization by Vector Space Methods
Optimization by Vector Space Methods
On Lagrangian Relaxation of Quadratic Matrix Constraints
SIAM Journal on Matrix Analysis and Applications
Polynomial Instances of the Positive Semidefinite and Euclidean Distance Matrix Completion Problems
SIAM Journal on Matrix Analysis and Applications
Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization
SIAM Journal on Optimization
Primal--Dual Path-Following Algorithms for Semidefinite Programming
SIAM Journal on Optimization
Strong Duality for Semidefinite Programming
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Cones of Matrices and Successive Convex Relaxations of Nonconvex Sets
SIAM Journal on Optimization
Semidefinite Programming Relaxation for NonconvexQuadratic Programs
Journal of Global Optimization
Distance Geometry Optimization for Protein Structures
Journal of Global Optimization
On the Performance of Polynomial-time CLIQUE Algorithms on Very Large Graphs
On the Performance of Polynomial-time CLIQUE Algorithms on Very Large Graphs
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
SDPPACK User''s Guide -- Version 0.9 Beta for Matlab 5.0.
An algorithmic analysis of multiquadratic and semidefinite programming problems
An algorithmic analysis of multiquadratic and semidefinite programming problems
Annals of Mathematics and Artificial Intelligence
A global continuation algorithm for solving binary quadratic programming problems
Computational Optimization and Applications
Provably near-optimal solutions for very large single-row facility layout problems
Optimization Methods & Software - GLOBAL OPTIMIZATION
Clustering for bioinformatics via matrix optimization
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
Multiclass image labeling with semidefinite programming
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
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Semidefinite programming (SDP) is currently one of the most active areas of research in optimization. SDP has attracted researchers from a wide variety of areas because of its theoretical and numerical elegance as well as its wide applicability. In this paper we present a survey of two major areas of application for SDP, namely discrete optimization and matrix completion problems.In the first part of this paper we present a recipe for finding SDP relaxations based on adding redundant constraints and using Lagrangian relaxation. We illustrate this with several examples. We first show that many relaxations for the max-cut problem (MC) are equivalent to both the Lagrangian and the well-known SDP relaxation. We then apply the recipe to obtain new strengthened SDP relaxations for MC as well as known SDP relaxations for several other hard discrete optimization problems.In the second part of this paper we discuss two completion problems, the positive semidefinite matrix completion problem and the Euclidean distance matrix completion problem. We present some theoretical results on the existence of such completions and then proceed to the application of SDP to find approximate completions. We conclude this paper with a new application of SDP to find approximate matrix completions for large and sparse instances of Euclidean distance matrices.