A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
The minimum-rank gram matrix completion via modified fixed point continuation method
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Composite splitting algorithms for convex optimization
Computer Vision and Image Understanding
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming
Numerical Algorithms
Computing real solutions of polynomial systems via low-rank moment matrix completion
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
An alternating direction method for second-order conic programming
Computers and Operations Research
A trust region method for solving semidefinite programs
Computational Optimization and Applications
Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials
Computational Optimization and Applications
Computational Optimization and Applications
Lower bounds on the global minimum of a polynomial
Computational Optimization and Applications
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We introduce a new class of algorithms for solving linear semidefinite programming (SDP) problems. Our approach is based on classical tools from convex optimization such as quadratic regularization and augmented Lagrangian techniques. We study the theoretical properties and we show that practical implementations behave very well on some instances of SDP having a large number of constraints. We also show that the “boundary point method” from Povh, Rendl, and Wiegele [Computing, 78 (2006), pp. 277-286] is an instance of this class.