This work analyzes constrained black box optimization in which the functions defining the problem are periodic with respect to some or all the variables. We show that the natural strategy of mapping trial points into the interval defined by the period in the Mesh Adaptive Direct Search (MADS) framework can be easily done in practice, … Read more
This paper describes a parallel space decomposition PSD technique for the mesh adaptive direct search MADS algorithm. MADS extends a generalized pattern search for constrained nonsmooth optimization problems. The objective of the present work is to obtain good solutions to larger problems than the ones typically solved by MADS. The new method PSD-MADS is an … Read more
We examine the local convergence of a sequential semidefinite programming approach for solving nonlinear programs with nonlinear semidefiniteness constraints. Known convergence results are extended to slightly weaker second order sufficient conditions and the resulting subproblems are shown to have local convexity properties that imply a weak form of self-concordance of the barrier subproblems. CitationPreprint, Mathematisches … Read more
In this paper, we present global and local convergence results for an interior-point method for nonlinear programming. The algorithm uses an $\ell_1$ penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’s strictly feasible interior-point method [6]. … Read more
Given r real functions F1 (x), . . . , Fr (x) and an integer p between 1 and r, the Low Order- Value Optimization problem (LOVO) consists of minimizing the sum of the functions that take the p smaller values. If (y1 , . . . , yr ) is a vector of data … Read more
A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix … Read more
We analyze a primal-dual interior-point method for nonlinear programming. We prove the global convergence for a wide class of problems under the standard assumptions on the problem. CitationTechnical Report ORFE-04-07, Department of ORFE, Princeton University, Princeton, NJ 08544ArticleDownload View PDF
The EM algorithm is a popular method for maximum likelihood estimation from incomplete data. This method may be viewed as a proximal point method for maximizing the log-likelhood function using an integral form of the Kullback-Leibler distance function. Motivated by this interpretation, we consider a proximal point method using an integral form of entropy-like distance … Read more
Recently, general definitions of pattern search methods for both unconstrained and linearly constrained optimization were presented. It was shown under mild conditions, that there exists a subsequence of iterates converging to a stationary point. In the unconstrained case, stronger results are derived under additional assumptions. In this paper, we present three small dimensioned examples showing … Read more
The linear support vector machine can be posed as a quadratic program in a variety of ways. In this paper, we look at a formulation using the two-norm for the misclassification error that leads to a positive definite quadratic program with a single equality constraint when the Wolfe dual is taken. The quadratic term is … Read more