This paper provides a framework for deriving payment mechanisms for intermittent, flexible and inflexible electricity generators who are dispatched according to the optimal solution of a stochastic program that minimizes the expected cost of generation plus deviation. The first stage corresponds to a pre-commitment decision, and the second stage corresponds to real-time generation that adapts … Read more
We present an improved approximation algorithm for the covering 0-1 integer program (CIP), a well-known problem as a natural generalization of the set cover problem. Our algorithm uses a primal-dual algorithm for CIP by Fujito (2004) as a subroutine and achieves an approximation ratio of (f- (f-1)/m) when m is greater than or equal to … Read more
In this paper, we introduce the Glider Routing and Trajectory Optimisation Problem (GRTOP), the problem of finding simultaneously optimal routes and trajectories for a fleet of gliders with the aim of surveying a set of locations. We propose a novel Mixed-Integer Nonlinear Programming (MINLP) formulation for the GRTOP, which simultaneously optimises the routes as well … Read more
Abstract—This paper discusses a hierarchical alternating direction method of multipliers (ADMM) approach for the unit commitment (UC) problem in a fully distributed manner. Decentralized unit commitment operation schemes have several advantages when compared with the traditional centralized management system for smart grid. Specifically, decentralized management is more flexible, less computationally intensive, and easier to implement … Read more
This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given … Read more
Potential-based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize … Read more
In the field of robust optimization uncertain data is modeled by uncertainty sets, i.e. sets which contain all relevant outcomes of the uncertain parameters. The complexity of the related robust problem depends strongly on the shape of the uncertainty set. Two popular classes of uncertainty are budgeted uncertainty and ellipsoidal uncertainty. In this paper we … Read more
Given two disjoint convex polyhedra, we look for a best approximation pair relative to them, i.e., a pair of points, one in each polyhedron, attaining the minimum distance between the sets. Cheney and Goldstein showed that alternating projections onto the two sets, starting from an arbitrary point, generate a sequence whose two interlaced subsequences converge … Read more
The alternating direction method of multipliers (ADMM) has been popularly used for a wide range of applications in the literature. When big datasets with high-dimensional variables are considered, subproblems arising from the ADMM must be solved inexactly even though theoretically they may have closed-form solutions. Such a scenario immediately poses mathematical ambiguities such as how … Read more
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework, which allows to construct different types of accelerated randomized methods for such problems and to prove convergence rate theorems for them. … Read more