A strategy is described for using linear programming (LP) to bound the solution set of the linear interval equation system that must be solved in the context of the interval-Newton method for deterministic global optimization. An implementation of this technique is described in detail, and several important issues are considered. These include selection of the interval corner required by the LP...

A strategy is described for using linear programming (LP) to bound the solution set of the linear interval equation system that must be solved in the context of the interval-Newton method for deterministic global optimization. An implementation of this technique is described in detail, and several important issues are considered. These include selection of the interval corner required by the LP...

A so-called Standard Bi-Quadratic Optimization Problem (StBQP) consists in minimizing a bi-quadratic form over the Cartesian product of two simplices (so this is different from a Bi-Standard QP where a quadratic function is minimized over the same set). An application example arises in portfolio selection. In this paper we present a bi-quartic formulation of StBQP, in order to get rid of the si...

Strategies involving smoothing of the objective function have been used to help solve difficult global optimization problems arising in molecular chemistry. This paper proposes a new smoothing approach and examines some basic issues in smoothing for molecular configuration problems. We first propose a new, simple algebraic way of smoothing the Lennard-Jones energy function, which is an importan...

In [8], G. David suggested a new type of global minimizer for the Mumford-Shah functional in R, for which the singular sets belong to a three parameters family of sets (0 < δ1, δ2, δ3 < π). We first derive necessary conditions satisfied by global minimizers of this family. Then we are led to study the first eigenvectors of the Laplace-Beltrami operator with Neumann boundary conditions on subdom...

In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We first extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions, and we propose a modification MSCA of this algorithm. We show that the implementation of the algorithm MSCA has the advantage of avoi...

We propose a novel two-level Boolean minimizer coming in succession to our previously developed minimizer BOOM, so we have named it BOOM-II. It is a combination of two minimizers, namely BOOM and FC-Min. Each of these two methods has its own area where it is most efficiently applicable. We have combined these two methods together to be able to solve all kinds of problems efficiently, independen...

We prove the stability of ball as global minimizer an attractive shape functional under volume constraint, by means mass transportation arguments. The exponent is $1/2$ and it sharp. Moreover, we use such result together with quantitative (possibly fractional) isoperimetric inequality to that a involving both repulsive term sufficiently large fixed suitable perimeter penalization.

We consider a multi-agent framework for distributed optimization where each agent in the network has access to a local convex function and the collective goal is to achieve consensus on the parameters that minimize the sum of the agents’ local functions. We propose an algorithm wherein each agent operates asynchronously and independently of the other agents in the network. When the local functi...

Many data-science problems can be formulated as an inverse problem, where the parameters are estimated by minimizing a proper loss function. When complicated black-box models involved, derivative-free optimization tools often needed. The ensemble Kalman filter (EnKF) is particle-based Bayesian algorithm originally designed for data assimilation. Recently, it has been applied to computational ef...