Driven by ambitious renewable portfolio standards, variable energy resources (such as wind and solar) are expected to impose unprecedented levels of uncertainty to power system operations. The current practice of planning operations with deterministic optimization tools may be ill-suited for a future where uncertainty is abundant. To overcome the reliability challenges associated with the large-scale … Read more
Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear programming (MSLP) problems often rely upon scenario trees to represent the underlying stochastic process. When this process exhibits stagewise independence, sampling-based techniques, particularly the … Read more
In radiation therapy treatment-plan optimization, selecting a set of clinical objectives that are tractable and parsimonious yet effective is a challenging task. In clinical practice, this is typically done by trial and error based on the treatment planner’s subjective assessment, which often makes the planning process inefficient and inconsistent. We develop the objective selection problem … Read more
We study a cutting-plane method for semidefinite optimization problems (SDOs), and supply a proof of the method’s convergence, under a boundedness assumption. By relating the method’s rate of convergence to an initial outer approximation’s diameter, we argue that the method performs well when initialized with a second-order-cone approximation, instead of a linear approximation. We invoke … Read more
This paper answers in affirmative the long-standing question of nonlinear analysis, concerning the existence of a continuous single-valued local selection of the right inverse to a locally Lipschitzian mapping. Moreover, we develop a much more general result, providing conditions for the existence of a continuous single-valued selection not only locally, but rather on any given … Read more
The paper observes a similarity between the stochastic optimal control of discrete dynamical systems and the learning multilayer neural networks. It focuses on contemporary deep networks with nonconvex nonsmooth loss and activation functions. The machine learning problems are treated as nonconvex nonsmooth stochastic optimization problems. As a model of nonsmooth nonconvex dependences, the so-called generalized … Read more
The superiorization methodology is intended to work with input data of constrained minimization problems, i.e., a target function and a constraints set. However, it is based on an antipodal way of thinking to the thinking that leads constrained minimization methods. Instead of adapting unconstrained minimization algorithms to handling constraints, it adapts feasibility-seeking algorithms to reduce … Read more
Given an undirected graph, we study the capacitated vertex separator problem which asks to find a subset of vertices of minimum cardinality, the removal of which induces a graph having a bounded number of pairwise disconnected shores (subsets of vertices) of limited cardinality. The problem is of great importance in the analysis and protection of … Read more
The minimum connectivity inference (MCI) problem represents an NP-hard generalization of the well-known minimum spanning tree problem. Given a set of vertices and a finite collection of subsets (of this vertex set), the MCI problem requires to find an edge set of minimal cardinality so that the vertices of each subset are connected. Although the … Read more
Empirical studies are fundamental in assessing the effectiveness of implementations of branch-and-bound algorithms. The complexity of such implementations makes empirical study difficult for a wide variety of reasons. Various attempts have been made to develop and codify a set of standard techniques for the assessment of optimization algorithms and their software implementations; however, most previous … Read more