相关论文: Robust recoverable 0-1 optimization problems under…

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms…

We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…

We consider the maximization problem of monotone submodular functions under an uncertain knapsack constraint. Specifically, the problem is discussed in the situation that the knapsack capacity is not given explicitly and can be accessed…

In industrial resource allocation problems, an initial planning stage may solve a nominal problem instance and a subsequent recovery stage may intervene to repair inefficiencies and infeasibilities due to uncertainty, e.g.\ machine failures…

Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…

This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this…

This paper addresses the transmission network expansion planning problem under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby the worst-case operating cost is accounted for…

In the present paper, a robust approach to a special class of convex feasibility problems is considered. By techniques of convex and variational analysis, conditions for the existence of robust feasible solutions and related error bounds…

In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint…

This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably…

In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…

We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…

We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem.

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed…

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions…

In this correspondence, we introduce a minimax regret criteria to the least squares problems with bounded data uncertainties and solve it using semi-definite programming. We investigate a robust minimax least squares approach that minimizes…

The "0-1 knapsack problem" stands as a classical combinatorial optimization conundrum, necessitating the selection of a subset of items from a given set. Each item possesses inherent values and weights, and the primary objective is to…

Uncertainty sets are at the heart of robust optimization (RO) because they play a key role in determining the RO models' tractability, robustness, and conservativeness. Different types of uncertainty sets have been proposed that model…

The multistage robust unit commitment (UC) is of paramount importance for achieving reliable operations considering the uncertainty of renewable realizations. The typical affine decision rule method and the robust feasible region method may…