Das Gupta, Shuvomoy Pavel, Lacra
Published in
Journal of Global Optimization

In this paper, we propose a multi-player extension of the minimum cost flow problem inspired by a transportation problem that arises in modern transportation industry. We associate one player with each arc of a directed network, each trying to minimize its cost function subject to the network flow constraints. In our model, the cost function can be...

Rahman, Hamidur Mahajan, Ashutosh
Published in
Journal of Global Optimization

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalitie...

Ivanov, Sergey V. Kibzun, Andrey I. Mladenović, Nenad Urošević, Dragan
Published in
Journal of Global Optimization

We consider the stochastic linear programming problem with quantile criterion and continuous distribution of random parameters. Using the sample approximation, we obtain a stochastic programming problem with discrete distribution of random parameters. It is known that the solution to this problem provides an approximate solution to the problem with...

Hai, L. P. Huerga, L. Khanh, P. Q. Novo, V.
Published in
Journal of Global Optimization

In this paper, we provide variants of the Ekeland variational principle for a type of approximate proper solutions of a vector equilibrium problem, whose final space is finite dimensional and partially ordered by a polyhedral cone. Depending on the choice of an approximation set that defines these solutions, we prove that they approximate suitably ...

Schlegel, Kevin
Published in
Journal of Global Optimization

We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the data points. This is at the core of kernel methods in machine learning as it makes the problem computationally t...

de Oliveira, Washington Alves Rojas-Medar, Marko Antonio Beato-Moreno, Antonio Hernández-Jiménez, Maria Beatriz
Published in
Journal of Global Optimization

If x∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^*$$\end{document} is a local minimum solution, then there exists a ball of radius r>0\documentclass[12pt]{minimal...

Dempe, Stephan Harder, Felix Mehlitz, Patrick Wachsmuth, Gerd
Published in
Journal of Global Optimization

In this paper, we show how a special class of inverse optimal control problems of elliptic partial differential equations can be solved globally. Using the optimal value function of the underlying parametric optimal control problem, we transfer the overall hierarchical optimization problem into a nonconvex single-level one. Unfortunately, standard ...

Ruiz, Ana B. Ruiz, Francisco Miettinen, Kaisa Delgado-Antequera, Laura Ojalehto, Vesa
Published in
Journal of Global Optimization

We propose a novel combination of an interactive multiobjective navigation method and a trade-off free way of asking and presenting preference information. The NAUTILUS Navigator is a method that enables the decision maker (DM) to navigate in real time from an inferior solution to the most preferred solution by gaining in all objectives simultaneou...

Kapoor, Shiva Lalitha, C. S.
Published in
Journal of Global Optimization

This paper is devoted to the study of Painlevé−Kuratowski convergence of constraint sets, minimal and efficient solution sets of a unified semi-infinite vector optimization problem. The convergence is established under the functional perturbations of objective function and constraint maps assuming the continuous convergence of the objective functio...

Gowda, M. Seetharama
Published in
Journal of Global Optimization

In the setting of a Euclidean Jordan algebra V with symmetric cone V+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_+$$\end{document}, corresponding to a linear tran...