With every law invariant coherent risk measure is associated its conditional analogue. In this paper we discuss lower and upper bounds for the corresponding nested (composite) formulations of law invariant coherent risk measures. In particular, we consider the Average Value-at-Risk and comonotonic risk measures. ArticleDownload View PDF
This paper presents a new accelerated variant of Nesterov’s method for solving composite convex optimization problems in which certain acceleration parameters are adaptively (and aggressively) chosen so as to substantially improve its practical performance compared to existing accelerated variants while at the same time preserve the optimal iteration-complexity shared by these methods. Computational results are … Read more
A generalized Weiszfeld method is proposed for the multi–facility location problem. The problem is relaxed using probabilistic assignments, and is decomposed into single facility location problems, that are coupled by these assignments, and can be solved in parallel. The probabilistic assignments are updated at each iteration, using the distances to the current centers. The method … Read more
We propose a first order interior point algorithm for a class of non-Lipschitz and nonconvex minimization problems with box constraints, which arise from applications in variable selection and regularized optimization. The objective functions of these problems are continuously differentiable typically at interior points of the feasible set. Our algorithm is easy to implement and the … Read more
Infrastructure-planning models are challenging because of their combination of different time scales: while planning and building the infrastructure involves strategic decisions with time horizons of many years, one needs an operational time scale to get a proper picture of the infrastructure’s performance and profitability. In addition, both the strategic and operational levels are typically subject … Read more
Triangulation of a three-dimensional point from $n\ge 2$ two-dimensional images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite programming relaxations. We then describe a sufficient condition and a polynomial time test for certifying when such a solution is optimal. This … Read more
In this paper, we address the optimal energy storage management and sizing problem in the presence of renewable energy and dynamic pricing. We formulate the problem as a stochastic dynamic programming problem that aims to minimize the long-term average cost of conventional generation used as well as investment in storage, if any, while satisfying all … Read more
Operations Research (OR) is the discipline of applying advanced analytical methods to help make better decisions (Horner (2003)). OR is characterized by its broad applicability and its interdisciplinary nature. Currently, in addition to mathematics, many other undergraduate programs such as management sciences, business, economics, electrical engineering, civil engineering, chemical engineering, and related fields, have incorporated … Read more
In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is … Read more
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The superiorization methodology is presented as a heuristic solver for a … Read more