A semi-smooth Newton method for general projection equations applied to the nearest correlation matrix problem

In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first present results concerning Clarke’s generalized Jacobian of the projection onto a closed and convex cone. We then describe the iterative process for the general cone case and establish … Read more

A Feasible method for Optimization with Orthogonality Constraints

Minimization with orthogonality constraints (e.g., $X^\top X = I$) and/or spherical constraints (e.g., $\|x\|_2 = 1$) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. … Read more