All feasible flows in potential-driven networks induce an orientation on the undirected graph underlying the network. Clearly, these orientations must satisfy two conditions: they are acyclic and there are no “dead ends” in the network, i.e. each source requires outgoing flows, each sink requires incoming flows, and each transhipment vertex requires both an incoming and … Read more
The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the usually employed relaxations are rather weak due to cycles … Read more
This article introduces new reduction techniques for the Steiner tree problem in graphs (SPG) and one of its most popular relatives, the maximum-weight connected subgraph problem. Several of the techniques generalize previous results from the literature. In particular, we introduce a generalization of the Steiner bottleneck distance—the arguably most important reduction concept for SPG. While … Read more
Sum-of-norms clustering is a clustering formulation based on convex optimization that automatically induces hierarchy. Multiple algorithms have been proposed to solve the optimization problem: subgradient descent by Hocking et al.\ \cite{hocking}, ADMM and ADA by Chi and Lange\ \cite{Chi}, stochastic incremental algorithm by Panahi et al.\ \cite{Panahi} and semismooth Newton-CG augmented Lagrangian method by Yuan … Read more
Liberalized gas markets in Europe are organized as entry-exit regimes so that gas trade and transport are decoupled. The decoupling is achieved via the announcement of technical capacities by the transmission system operator (TSO) at all entry and exit points of the network. These capacities can be booked by gas suppliers and customers in long-term … Read more
This paper presents necessary and sufficient optimality conditions for discrete-continuous nonlinear optimization problems including mixed-integer nonlinear problems. This theory does not utilize an extension of the Lagrange theory of continuous optimization but it works with certain max functionals for a separation of two sets where one of them is nonconvex. These functionals have the advantage … Read more
In this paper, we consider the rate of convergence with sample average approximation (SAA) under heavy tailed distributions and quantify it under both independent identically distributed (iid) sampling and non-iid sampling. We rst derive the polynomial rate of convergence for random variable under iid sampling. Then, the uniform polynomial rates of convergence for both random … Read more
Using the weighted geometric series expansion, it is shown how integer programming can be solved by evaluating complex path integrals based on a multi-path version of Cauchy’s integral formula. In contrast to existing generating function approaches, the algorithm relies only on complex quadrature and no algebraic techniques are needed. In view of fast implementations of … Read more
Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the transition probabilities significantly increases the computational complexity of solving robust MDPs, which severely limits their scalability. This paper describes new efficient algorithms for solving the … Read more
In semidefinite programming the dual may fail to attain its optimal value and there could be a duality gap, i.e., the primal and dual optimal values may differ. In a striking paper, Ramana proposed a polynomial size extended dual that does not have these deficiencies and yields a number of fundamental results in complexity theory. … Read more