Approximation Guarantees for Min-max-min Robust Optimization and K-Adaptability under Objective Uncertainty

In this work we investigate the min-max-min robust optimization problem for binary problems with uncertain cost-vectors. The idea of the approach is to calculate a set of k feasible solutions which are worst-case optimal if in each possible scenario the best of the k solutions is implemented. It is known that the min-max-min robust problem … Read more

General Polyhedral Approximation of Two-Stage Robust Linear Programming

 We consider two-stage robust linear programs with a budget of uncertainty for the righthand side. In this scenario set, which is frequently used in robust optimization, the uncertain righthand side for each row lies in an interval and the relative increases summed over all rows are less than a budget $$\Gamma$$. We develop a … Read more

D-optimal Data Fusion: Exact and Approximation Algorithms

We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that the DDF problem is NP-hard and has no constant-factor polynomial-time approximation algorithm unless P = NP. … Read more

A $\sqrt{5}/2$-approximation algorithm for optimal piecewise linear approximations of bounded variable products

We investigate the optimal piecewise linear approximation of the bivariate product $xy$ over rectangular domains. More precisely, our aim is to minimize the number of simplices in the triangulation underlying the approximation, while respecting a prescribed approximation error. First, we show how to construct optimal triangulations consisting of up to five simplices. Using … Read more

Approximation algorithm for the two-stage stochastic set multicover problem with simple resource

We study a two-stage, finite-scenarios stochastic version of the set multicover problem, where there is uncertainty about a demand for each element to be covered and the penalty cost is imposed linearly on the shortfall in each demand. This problem is NP-hard and has an application in shift scheduling in crowdsourced delivery services. For this … Read more

Sequential Competitive Facility Location: Exact and Approximate Algorithms

We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation … Read more