We study the problem of allocating doctors to primary health centers. We model the problem as a multi-period uncapacitated facility location problem under uncertainty. The problem is unconventional in that the uncertainty is in the number and period of availability of doctors. We use a minmax regret approach to solve the problem. We present solution techniques using local search and tabu search...

In previous work, the determination of uncertainty models via minimum norm model validation is based on a single set of input and output measurement data. Since uncertainty bounds at each frequency is directionally dependent for multivariable systems, this will lead to optimistic uncertainty levels. In addition, the design freedom in the uncertainty model has not been utilized to further reduce...

Abstract: This paper considers the adaptive control of a class of nonlinear discrete time system with nonlinearly parametrized functions. In particular, the focus is on concave or convex parametrizations with unknown parameters. The solutions involved 2 tuning functions which are determined by a minmax optimization approach much like the continuous time counterparts found in the literature. Dir...

Feedback control of fluids is often achieved with limited state measurements. Effective approaches utilize compensators, which can be computed using linear quadratic Gaussian (LQG) or MinMax control designs. However, to achieve real-time control algorithms, these compensators must have low computational complexity. Model reduction methods are a natural choice to build reduced-order compensators...

The paper studies the problem of reachability for linear systems in the presence of uncertain (unknown but bounded) input disturbances, which may also be interpreted as the action of an adversary in a gametheoretic setting. It defines possible notions of reachability under uncertainty emphasizing the differences between open-loop and closed-loop control. Solution schemes for calculating reachab...

Traditional distance metric learning with side information usually formulates the objectives using the covariance matrices of the data point pairs in the two constraint sets of must-links and cannotlinks. Because the covariance matrix computes the sum of the squared l2-norm distances, it is prone to both outlier samples and outlier features. To develop a robust distance metric learning method, ...

In game theory and in particular in the theory of stochastic games, we encounter systems of polynomial equalities and inequalities. We start with a few examples. The first example relates to the minmax value and optimal strategies of a two-person zero-sum game with finitely many strategies. Consider a twoperson zero-sum game represented by a k ×m matrix A = (aij), 1 ≤ i ≤ k and 1 ≤ j ≤ m. The n...

This paper investigates, for the first time in the literature, the approximation of minmax (regret) versions of classical problems like shortest path, minimum spanning tree, and knapsack. For a constant number of scenarios, we establish fully polynomial-time approximation schemes for the min-max versions of these problems, using relationships between multi-objective and min-max optimization. Us...

The king of refinements of Nash equilibrium is trembling hand perfection. We show that it is NP-hard and Sqrt-Sum-hard to decide if a given pure strategy Nash equilibrium of a given three-player game in strategic form with integer payoffs is trembling hand perfect. Analogous results are shown for a number of other solution concepts, including proper equilibrium, (the strategy part of) sequentia...

Today, IEEE 802.11 wireless LANs (WLANs) are widely deployed throughout the world. It is known that static channel assignments are not sufficient for these networks due to traffic variations. However, in order to maintain compatibility with the existing protocol standards, it is not possible to employ dynamic channel allocation methods to handle traffic-load fluctuations. Rather, adaptive assig...