| Typical placement objectives involve reducing net-cut cost or minimizing wirelength. Congestion minimization is the least understood, however, it models routability most accurately. In this paper, we study the congestion minimization problem during placement. First, we show that a global placement with minimum wirelength has minimum total congestion. We show that minimizing wirelength may (an...

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm minimization problem. However, soft-thresholding of singular values leads to the elimination of important information about the sensed matrix. Weighted nucl...

Scatter search (SS) is a metaheuristic framework that explores solution spaces by evolving a set of reference points. These points (solutions) are initially generated with a diversification method and the evolution of these reference points is induced by the application of four methods: subset generation, combination, improvement and update. In this paper, we consider the application of the SS ...

This paper discusses a generalization of the function transformation scheme for global energy minimization applied to the molecular conformation problem. A mathematical theory for the method as a special continuation approach to global o p timization is established. We show that the method can transform a nonlinear objective function into a class of &dua l ly deformed, but “smoother” or “easier...

We consider the expected residual minimization formulation of the stochastic R0 matrix linear complementarity problem. We show that the involved matrix being a stochastic R0 matrix is a necessary and sufficient condition for the solution set of the expected residual minimization problem to be nonempty and bounded. Moreover, local and global error bounds are given for the stochastic R0 matrix li...

Two fundamental problems of machine learning misclassi cation minimization and feature selection are formulated as the minimization of a concave function on a polyhedral set Other formulations of these problems utilize linear programs with equilibrium constraints which are generally intractable In contrast for the proposed concave minimization formulation a successive linearization algorithm wi...

In this article, we address the interpolation problem of data points per regular L1spline polynomial curve that is invariant under a rotation of the data. We iteratively apply a minimization method on five data, belonging to a sliding window, in order to obtain this interpolating curve. We even show in the Ck-continuous interpolation case that this local minimization method preserves well the l...