39 research outputs found
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
Structured Low Rank Matrix Optimization Problems: A Penalty Approach
Ph.DDOCTOR OF PHILOSOPH
A Semismooth Newton-CG Augmented Lagrangian Method for Large Scale Linear and Convex Quadratic SDPS
Ph.DDOCTOR OF PHILOSOPH
A Majorization Algorithm for Constrained Correlation Matrix Approximation
We desire to find a correlation matrix of a given rank that is as close as possible to an input matrix R, subject to the constraint that specified elements in must be zero. Our optimality criterion is the weighted Frobenius norm of the approximation error, and we use a constrained majorization algorithm to solve the problem. Although many correlation matrix approximation approaches have been proposed, this specific problem, with the rank specification and the constraints, has not been studied until now. We discuss solution feasibility, convergence, and computational effort. We also present several examples