Computational Guarantees for Restarted PDHG for LP based on “Limiting Error Ratios” and LP Sharpness

In recent years, there has been growing interest in solving linear optimization problems – or more simply “LP” – using first-order methods in order to avoid the costly matrix factorizations of traditional methods for huge-scale LP instances. The restarted primal-dual hybrid gradient method (PDHG) – together with some heuristic techniques – has emerged as a … Read more

On the Relation Between LP Sharpness and Limiting Error Ratio and Complexity Implications for Restarted PDHG

There has been a recent surge in development of first-order methods (FOMs) for solving huge-scale linear programming (LP) problems. The attractiveness of FOMs for LP stems in part from the fact that they avoid costly matrix factorization computation. However, the efficiency of FOMs is significantly influenced – both in theory and in practice – by … Read more

Hardness of pricing routes for two-stage stochastic vehicle routing problems with scenarios

The vehicle routing problem with stochastic demands (VRPSD) generalizes the classic vehicle routing problem by considering customer demands as random variables. Similarly to other vehicle routing variants, state-of-the-art algorithms for the VRPSD are often based on set-partitioning formulations, which require efficient routines for the associated pricing problems. However, all these set-partitioning-based approaches have strong assumptions … Read more

Robust Two-Dose Vaccination Schemes and the Directed b-Matching Problem

In light of the recent pandemic and the shortage of vaccinations during their roll-out, questions arose regarding the best strategy to achieve immunity throughout the population by adjusting the time gap between the two necessary vaccination doses. This strategy has already been studied from different angles by various researches. However, the deliveries of vaccination doses … Read more

Recognition of Facets for Knapsack Polytope is DP-complete

DP  is a complexity class that is the class of all languages that are the intersection of a language in NP and a language in co-NP, as coined by Papadimitriou and Yannakakis. In this paper, we will establish that, recognizing a facet for the knapsack polytope is DP-complete, as conjectured by Hartvigsen and Zemel in … Read more

Using Taylor-Approximated Gradients to Improve the Frank-Wolfe Method for Empirical Risk Minimization

\(\) The Frank-Wolfe method has become increasingly useful in statistical and machine learning applications, due to the structure-inducing properties of the iterates, and especially in settings where linear minimization over the feasible set is more computationally efficient than projection. In the setting of Empirical Risk Minimization — one of the fundamental optimization problems in statistical … Read more

Deciding the Feasibility of a Booking in the European Gas Market is coNP-hard

We show that deciding the feasibility of a booking (FB) in the European entry-exit gas market is coNP-hard if a nonlinear potential-based flow model is used. The feasibility of a booking can be characterized by polynomially many load flow scenarios with maximum potential-difference, which are computed by solving nonlinear potential-based flow models. We use this … Read more