Bounds in multi-horizon stochastic programs

In this paper, we present bounds for multi-horizon stochastic optimization problems, a class of problems introduced in [16] relevant in many industry-life applications tipically involving strategic and operational decisions on two different time scales. After providing three general mathematical formulations of a multi-horizon stochastic program, we extend the definition of the traditional Expected Value problem … Read more

A Branch-and-Bound based Algorithm for Nonconvex Multiobjective Optimization

A new branch-and-bound based algorithm for smooth nonconvex multiobjective optimization problems with convex constraints is presented. The algorithm computes an $(\varepsilon,\delta)$-approximation of all globally optimal solutions. We introduce the algorithm which uses selection rules, discarding and termination tests. The discarding tests are the most important aspect, as they examine in different ways whether a box … Read more

A Simple Nearly-Optimal Restart Scheme For Speeding-Up First-Order Methods

We present a simple scheme for restarting first-order methods for convex optimization problems. Restarts are made based only on achieving specified decreases in objective values, the specified amounts being the same for all optimization problems. Unlike existing restart schemes, the scheme makes no attempt to learn parameter values characterizing the structure of an optimization problem, … Read more

Radar Waveform Optimization for Joint Radar Communications Performance

We develop and present a radar waveform design method that optimizes the spectral shape of the radar waveform so that joint performance of a cooperative radar-communications system is maximized. The continuous water-filling (WF) spectralmask shaping method presented in this paper is based the previously derived spectral-mask shaping technique. However, the method presented in this paper … Read more

An algorithm for computing Frechet means on the sphere

For most optimisation methods an essential assumption is the vector space structure of the feasible set. This condition is not fulfilled if we consider optimisation problems over the sphere. We present an algorithm for solving a special global problem over the sphere, namely the determination of Frechet means, which are points minimising the mean distance … Read more

ADMM for Multiaffine Constrained Optimization

We propose an expansion of the scope of the alternating direction method of multipliers (ADMM). Specifically, we show that ADMM, when employed to solve problems with multiaffine constraints that satisfy certain easily verifiable assumptions, converges to the set of constrained stationary points if the penalty parameter in the augmented Lagrangian is sufficiently large. When the … Read more

A Benders decomposition method for locating stations in a one-way electric car sharing system under demand uncertainty

We focus on a problem of locating recharging stations in one-way station based electric car sharing systems which operate under demand uncertainty. We model this problem as a mixed integer stochastic program and develop a Benders decomposition algorithm based on this formulation. We integrate a stabilization procedure to our algorithm and conduct a large-scale experimental … Read more

A Computational Investigation on the Strength of Dantzig-Wolfe Reformulations

In Dantzig-Wolfe reformulation of an integer program one convexifies a subset of the constraints, leading to potentially stronger dual bounds from the respective linear programming relaxation. As the subset can be chosen arbitrarily, this includes the trivial cases of convexifying no and all constraints, resulting in a weakest and strongest reformulation, respectively. Our computational study … Read more

A Riemannian Conjugate Gradient Algorithm with Implicit Vector Transport for Optimization on the Stiefel Manifold

In this paper, a reliable curvilinear search algorithm for solving optimization problems over the Stiefel manifold is presented. This method is inspired by the conjugate gradient method, with the purpose of obtain a new direction search that guarantees descent of the objective function in each iteration. The merit of this algorithm lies in the fact … Read more

Network Models for Multiobjective Discrete Optimization

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design tools and techniques for exploiting the network model in … Read more