Given an existing Mobile Edge Cloud (MEC) network including virtualization facilities of limited capacity, and a set of mobile Access Points (AP) whose data traffic demand changes over time, we aim at finding plans for assigning APs traffic to MEC facilities so that the demand of each AP is satisfied and MEC facility capacities are … Read more
This paper explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions $f$ at a given point, it is shown that for quadratic functions there exists exactly one invariant descent direction in the strictly convex case and generally none in the nondegenerate … Read more
The simple integer recourse (SIR) function of a decision variable is the expectation of the integer round-up of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two stage stochastic linear programming. Structural properties and approximations of SIR … Read more
Bundle methods determine the next candidate point as the minimizer of a cutting model augmented with a proximal term. We propose a dynamic approach for choosing a quadratic proximal term based on subgradient information from past evaluations. For the special case of convex quadratic functions, conditions are studied under which this actually reproduces the Hessian. … Read more
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from … Read more
Problem of finding the closest stable matrix for a dynamical system has many applications. It is well studied both for continuous and discrete-time systems, and the corresponding optimization problems are formulated for various matrix norms. As a rule, non-convexity of these formulations does not allow finding their global solutions. In this paper, we analyze positive … Read more
In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. … Read more
In this paper, we present the proximal-proximal-gradient method (PPG), a novel optimization method that is simple to implement and simple to parallelize. PPG generalizes the proximal-gradient method and ADMM and is applicable to minimization problems written as a sum of many differentiable and many non-differentiable convex functions. The non-differentiable functions can be coupled. We furthermore … Read more
There is an undeniable global shortage of skillful nurses. This is a problem of high priority, which is correlated to workforce management issues. These issues can be palliated by increasing nurses’ satisfaction based on flexible rosters using automated nurse rostering. This paper in concerned with nurse rostering based on constraint programming by satisfying global constraints, … Read more
The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, while well-known monotone risk measures, such as VaR and … Read more