The idea of k-adaptability in two-stage robust optimization is to calculate a fixed number k of second-stage policies here-and-now. After the actual scenario is revealed, the best of these policies is selected. This idea leads to a min-max-min problem. In this paper, we consider the case where no first stage variables exist and propose to use this approach to solve combinatorial optimization pr...

A bipartite graph G(U, V ;E) that admits a perfect matching is given. One player imposes a permutation π over V , the other player imposes a permutation σ over U . In the greedy matching algorithm, vertices of U arrive in order σ and each vertex is matched to the lowest (under π) yet unmatched neighbor in V (or left unmatched, if all its neighbors are already matched). The obtained matching is ...

This paper provides characterization theorems for preferences that can be represented by U(x1, ..., xn)=min{xk}, U(x1, ..., xn)=max{xk}, U(x1, ..., xn)=; u(xk), or combinations of these functionals. The main assumption is partial separability, where changing a common component of two vectors does not reverse strict preferences, but may turn strict preferences into indifference. We discuss appli...

The min-max kernel is a generalization of the popular resemblance kernel (which is designed for binary data). In this paper, we demonstrate, through an extensive classification study using kernel machines, that the min-max kernel often provides an effective measure of similarity for nonnegative data. As the min-max kernel is nonlinear and might be difficult to be used for industrial application...

We propose algorithms for a special type of geometric facility location problem in which customers may choose not to use the facility. We minimize the maximum cost incurred by a customer, where the cost itself is a minimum between two costs, according to whether the facility is used or not. We therefore call this type of location problem a min-max-min geometric facility location problem. As a f...

We study the application of min-max propagation, a variation of belief propagation, for approximate min-max inference in factor graphs. We show that for “any” highorder function that can be minimized inO(ω), the min-max message update can be obtained using an efficient O(K(ω + log(K)) procedure, where K is the number of variables. We demonstrate how this generic procedure, in combination with e...

Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more fine-tuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to exi...

Linearly combining multiple biomarkers is a common practice that can provide better diagnostic performance. When the number of sufficiently high, computational burden problem arises. Liu et al. proposed distribution-free approach (min–max approach) linearly combines minimum and maximum values biomarkers, involving only single coefficient search. However, combination alone may not be sufficient ...

In this paper we show that the problem of minimizing a nonlinear objective function subject to a system of fuzzy relational equations with max-min composition can be reduced to a 0-1 mixed integer programming problem. The reduction method can be extended to the case of fuzzy relational equations with max-T composition as well as those with more general composition.