Some perturbation theory for linear programming
Mathematical Programming: Series A and B
Linear programming, complexity theory and elementary functional analysis
Mathematical Programming: Series A and B
An exact duality theory for semidefinite programming and its complexity implications
Mathematical Programming: Series A and B
Semidefinite programming relaxations for the graph partitioning problem
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
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 the Convergence of the Central Path in Semidefinite Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
Strong Duality for Semidefinite Programming
SIAM Journal on Optimization
Condition-Based Complexity of Convex Optimization in Conic Linear Form via the Ellipsoid Algorithm
SIAM Journal on Optimization
On the Local Convergence of a Predictor-Corrector Method for Semidefinite Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
Addendum to "Presolve Analysis of Linear Programs Prior to Applying an Interior Point Method"
INFORMS Journal on Computing
An algorithmic analysis of multiquadratic and semidefinite programming problems
An algorithmic analysis of multiquadratic and semidefinite programming problems
Semidefinite Approximations for Global Unconstrained Polynomial Optimization
SIAM Journal on Optimization
LMI Approximations for Cones of Positive Semidefinite Forms
SIAM Journal on Optimization
SIAM Journal on Optimization
Progress in the dual simplex method for large scale LP problems: practical dual phase 1 algorithms
Computational Optimization and Applications
Set Intersection Theorems and Existence of Optimal Solutions
Mathematical Programming: Series A and B
Invariance and efficiency of convex representations
Mathematical Programming: Series A and B
Complete characterizations of stable Farkas’ lemma and cone-convex programming duality
Mathematical Programming: Series A and B
On the Closedness of the Linear Image of a Closed Convex Cone
Mathematics of Operations Research
A stable primal---dual approach for linear programming under nondegeneracy assumptions
Computational Optimization and Applications
Generating and measuring instances of hard semidefinite programs
Mathematical Programming: Series A and B
Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions
SIAM Journal on Optimization
On the Slater condition for the SDP relaxations of nonconvex sets
Operations Research Letters
An Exact Duality Theory for Semidefinite Programming Based on Sums of Squares
Mathematics of Operations Research
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The elegant theoretical results for strong duality and strict complementarity for linear programming, LP, lie behind the success of current algorithms. In addition, preprocessing is an essential step for efficiency in both simplex type and interior-point methods. However, the theory and preprocessing techniques can fail for cone programming over nonpolyhedral cones. We take a fresh look at known and new results for duality, optimality, constraint qualifications, CQ, and strict complementarity, for linear cone optimization problems in finite dimensions. One theme is the notion of minimal representation of the cone and the constraints. This provides a framework for preprocessing cone optimization problems in order to avoid both the theoretical and numerical difficulties that arise due to the (near) loss of the strong CQ, strict feasibility. We include results and examples on the surprising theoretical connection between duality gaps in the original primal-dual pair and lack of strict complementarity in their homogeneous counterpart. Our emphasis is on results that deal with Semidefinite Programming, SDP.