Four NP-hard optimization problems on graphs are studied: The vertex separator problem, the edge separator problem, the maximum clique problem, and the maximum independent set problem. We show that the vertex separator problem is equivalent to a continuous bilinear quadratic program. This...

Recently an affine scaling, interior point algorithm ASL was developed for box constrained optimization problems with a single linear constraint (Gonzalez-Lima et al., SIAM J. Optim. 21:361–390, <CitationRef CitationID="CR7">2011</CitationRef>). This note extends the algorithm to handle more general polyhedral constraints. With a line...</citationref>

Methods are developed and analyzed for estimating the distance to a local minimizer of a nonlinear programming problem. One estimate, based on the solution of a constrained convex quadratic program, can be used when strict complementary slackness and the second-order sufficient optimality...

We propose a new gradient method for quadratic programming, named SDC, which alternates some steepest descent (SD) iterates with some gradient iterates that use a constant steplength computed through the Yuan formula. The SDC method exploits the asymptotic spectral behaviour of the Yuan...

This paper develops a Bregman operator splitting algorithm with variable stepsize (BOSVS) for solving problems of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\min\{\phi(Bu) +1/2\|Au-f\|_{2}^{2}\}$</EquationSource> </InlineEquation>, where ϕ may be nonsmooth. The original Bregman Operator Splitting (BOS) algorithm employed a fixed stepsize, while BOSVS uses a...</equationsource></inlineequation>

Techniques for estimating the condition number of a nonsingular matrix are developed. It is shown that Hager’s 1-norm condition number estimator is equivalent to the conditional gradient algorithm applied to the problem of maximizing the 1-norm of a matrix-vector product over the unit sphere...