Related papers: Min-Max-Min Robustness for Combinatorial Problems …
As most robust combinatorial min-max and min-max regret problems with discrete uncertainty sets are NP-hard, research into approximation algorithm and approximability bounds has been a fruitful area of recent work. A simple and well-known…
We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method applicable to many optimization problems. Our approach takes advantage of hidden…
Biclustering is the task of simultaneously clustering the rows and columns of the data matrix into different subgroups such that the rows and columns within a subgroup exhibit similar patterns. In this paper, we consider the case of…
The regular set tolerance is an important term in sensitivity analysis. For combinatorial sum problems, e.g., the Traveling Salesman Problem, Shortest Path Problem and Minimum Spanning Tree Problem, it determines how much the sum of the…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…
In this paper a class of optimization problems with uncertain linear constraints is discussed. It is assumed that the constraint coefficients are random vectors whose probability distributions are only partially known. Possibility theory is…
In a random model of minimum cost bipartite matching based on exponentially distributed edge costs, we show that the distribution of the cost of the optimal solution can be computed efficiently. The distribution is represented by its moment…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…
In two-stage robust optimization the solution to a problem is built in two stages: In the first stage a partial, not necessarily feasible, solution is exhibited. Then the adversary chooses the "worst" scenario from a predefined set of…
Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio…
Classical deterministic optimal control problems assume full information about the controlled process. The theory of control for general partially-observable processes is powerful, but the methods are computationally expensive and typically…
In this paper, we provide a generic anytime lower bounding procedure for minmax regret optimization problems. We show that the lower bound obtained is always at least as accurate as the lower bound recently proposed by Chassein and Goerigk…
We study the design of resilient and reliable communication networks in which a signal can be transferred only up to a limited distance before its quality falls below an acceptable threshold. When excessive signal degradation occurs,…
We study the problem of incorporating risk while making combinatorial decisions under uncertainty. We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly…
This paper considers a recoverable robust single-machine scheduling problem under polyhedral uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, many applications require exact solutions, as approximate…
We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the…
This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…