The problem of calculating the best approximating straight line--in the sense of Chebyshev--to a finite set of points in R" is considered. Firstand second-order optimality conditions are derived and analysed. Lipschitz optimization techniques can be used to find a global minimizer.

Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem. In practice this approach works well, and it is often computationally faster than standard convex solvers such as proximal gradient methods. Nevertheless, it...

The double-covering map udc : R 2 → R is given by udc(x) = 1 √ 2|x| ( x2 2 − x12 2x1x2 ) in cartesian coordinates. This paper examines the conjecture that udc is the global minimizer of the Dirichlet energy I(u) = ∫ B |∇u| dx among allW 1,2 mappings u of the unit ball B ⊂ R satisfying (i) u = udc on ∂B, and (ii) det∇u = 1 almost everywhere. Let the class of such admissible maps be A. The chief ...

In this short note, the objective of which is essentially pedagogical, we show that in the well-known problem which consists of minimizing the rank of a matrix, every admissible point is a local minimizer. Hence, in this problem like in various other ones, only global minimization matters.

In this paper we establish necessary as well as sufficient conditions for a given feasible point to be a global minimizer of smooth minimization problems with mixed variables. These problems, for instance, cover box constrained smooth minimization problems and bivalent optimization problems. In particular, our results provide necessary global optimality conditions for difference convex minimiza...

The most widely used guaranteed methods for global optimization are probably the interval-based branch-and-bound techniques. In these techniques, we start with a single box { the entire function domain { as a possible location of the global minimizer points, and then, in each step, subdivide some of the boxes, use interval computations to compute the enclosure F (X); F(X)] f(X) of the range f(X...

Minimizing the Lennard-Jones potential, the most-studied model problem for molecular conformation, is an unconstrained global optimization problem with a large number of local minima. In this paper, the problem is reformulated as an equality constrained nonlinear programming problem with only linear constraints. This formulation allows the solution to approached through infeasible configuration...

In this paper we consider a global optimization method for space trajectory design problems. The method, which actually aims at finding not only the global minimizer but a whole set of low-lying local minimizers (corresponding to a set of different design options), is based on a domain decomposition technique where each subdomain is evaluated through a procedure based on the evolution of a popu...

Abstract We study a model for adversarial classification based on distributionally robust chance constraints. show that under Wasserstein ambiguity, the aims to minimize conditional value-at-risk of distance misclassification, and we explore links models proposed earlier maximum-margin classifiers. also provide reformulation linear classification, it is equivalent minimizing regularized ramp lo...

The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- higher-dimensional problems when Manhattan distance is considered. Before we propose exact method, start with single-facility obtain global minimizer using a statistical approach. Then, an method dev...