On the Global Optimality for Linear Constrained Rank Minimization Problem

The rank minimization with linear equality constraints has two closely related models, the low rank approximation model, that is to find the best rank-k approximation of a matrix satisfying the linear constraints, and its corresponding factorization model. The latter one is an unconstrained nonlinear least squares problem and hence enjoys a few fast first-order methods … Read more

A well-posed shooting algorithm for optimal control problems with singular arcs

In this article we establish for the first time the well-posedness of the shooting algorithm applied to optimal control problems for which all control variables enter linearly in the Hamil- tonian. We start by investigating the case having only initial-final state constraints and free control variable, and afterwards we deal with control bounds. The shooting … Read more

Partially affine control problems: second order conditions and a well-posed shooting algorithm

This paper deals with optimal control problems for systems that are affine in one part of the control variables and nonlinear in the rest of the control variables. We have finitely many equality and inequality constraints on the initial and final states. First we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, … Read more