Complexity Aspects of Local Minima and Related Notions

We consider the notions of (i) critical points, (ii) second-order points, (iii) local minima, and (iv) strict local minima for multivariate polynomials. For each type of point, and as a function of the degree of the polynomial, we study the complexity of deciding (1) if a given point is of that type, and (2) if … Read more

Selective Maximum Coverage and Set Packing

In this paper we introduce the selective maximum coverage and the selective maximum set packing problem and variants of them. Both problems are strongly related to well studied problems such as maximum coverage, set packing, and (bipartite) hypergraph matching. The two problems are given by a collection of subsets of a ground set and index … Read more

The Multi-Stop Station Location Problem

We introduce the (directed) multi-stop station location problem. The goal is to install stations such that ordered (multi-)sets of stops can be traversed with respect to range restrictions that are reset whenever a station is visited. Applications arise in telecommunications and transportation, e.g., charging station placement problems. The problem generalizes several network optimization problems such … Read more

Complexity of cutting planes and branch-and-bound in mixed-integer optimization

We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash to the nonlinear setting which shows that for convex 0/1 problems, CP … Read more

Computing Technical Capacities in the European Entry-Exit Gas Market is NP-Hard

As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes … Read more

Stochastic Dual Dynamic Programming for Multistage Stochastic Mixed-Integer Nonlinear Optimization

In this paper, we study multistage stochastic mixed-integer nonlinear programs (MS-MINLP). This general class of problems encompasses, as important special cases, multistage stochastic convex optimization with \emph{non-Lipschitz-continuous} value functions and multistage stochastic mixed-integer linear optimization. We develop stochastic dual dynamic programming (SDDP) type algorithms with nested decomposition, deterministic sampling, and stochastic sampling. The key ingredient … Read more

Deciding Feasibility of a Booking in the European Gas Market on a Cycle is in P for the Case of Passive Networks

We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks that are passive, i.e., do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow … Read more

Minimizing Airplane Boarding Time

The time it takes passengers to board an airplane is known to influence the turn-around time of the aircraft and thus bears a significant cost-saving potential for airlines. Although minimizing boarding time therefore is the most important goal from an economic perspective, previous efforts to design efficient boarding strategies apparently never tackled this task directly. … Read more

Vertex ordering with optimal number of adjacent predecessors

In this paper, we study the complexity of the selection of a graph discretization order with a stepwise linear cost function.Finding such vertex ordering has been proved to be an essential step to solve discretizable distance geometry problems (DDGPs). DDGPs constitute a class of graph realization problems where the vertices can be ordered in such … Read more

Inexact proximal stochastic second-order methods for nonconvex composite optimization

In this paper, we propose a framework of Inexact Proximal Stochastic Second-order (IPSS) methods for solving nonconvex optimization problems, whose objective function consists of an average of finitely many, possibly weakly, smooth functions and a convex but possibly nons- mooth function. At each iteration, IPSS inexactly solves a proximal subproblem constructed by using some positive … Read more