On the computation of C* certificates
Journal of Global Optimization
Algorithms and theory of computation handbook
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
A trust region method for solving semidefinite programs
Computational Optimization and Applications
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We propose a new iterative approach for solving linear programs over convex cones. Assuming that Slater's condition is satisfied, the conic problem is transformed to the minimization of a convex differentiable function in the primal-dual space. This function shows similarities with the augmented Lagrangian function and is called “augmented primal-dual function” or “apd-function”. The evaluation of the function and its derivative is cheap if the projection of a given point onto the cone can be computed cheaply, and if the projection of a given point onto the affine subspace defining the primal problem can be computed cheaply. For the special case of a semidefinite program, a certain regularization of the apd-function is analyzed. Numerical examples minimizing the apd-function with a conjugate gradient method illustrate the potential of the approach.