The Distance Geometry Problem in three dimensions consists in finding an embedding in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${\mathbb{R}^3}$$</EquationSource> </InlineEquation> of a given nonnegatively weighted simple undirected graph such that edge weights are equal to the corresponding Euclidean distances in the embedding. This is a continuous search problem...</equationsource></inlineequation>

An appropriate distance is an essential ingredient in various real-world learning tasks. Distance metric learning proposes to study a metric, which is capable of reflecting the data configuration much better in comparison with the commonly used methods. We offer an algorithm for simultaneous...

Penalty function is an important tool in solving many constrained optimization problems in areas such as industrial design and management. In this paper, we study exactness and algorithm of an objective penalty function for inequality constrained optimization. In terms of exactness, this...

This paper aims to study a broad class of generalized semi-infinite programming problems with (upper and lower level) objectives given as the difference of two convex functions, and (lower level) constraints described by a finite number of convex inequalities and a set constraints. First, we are...

This paper is focused on computational study of continuous approach for the maximum weighted clique problem. The problem is formulated as a continuous optimization problem with a nonconvex quadratic constraint given by the difference of two convex functions (d.c. function). The proposed approach...

The pooling problem is an extension of the minimum cost network flow problem where the composition of the flow depends on the sources from which it originates. At each source, the composition is known. In all other nodes, the proportion of any component is given as a weighted average of its...

We consider vector models for complex systems with spatially distributed elements which arise in communication and transportation networks. In order to describe the flow distribution within such a network, we utilize the equilibrium approach, which extends the shortest path one. Being based on...

A new method is described for computing nonlinear convex and concave relaxations of the solutions of parametric ordinary differential equations (ODEs). Such relaxations enable deterministic global optimization algorithms to be applied to problems with ODEs embedded, which arise in a wide variety...

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative entropy are defined using the Kullback-Leibler divergence,...

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD...