In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this … Read more
A method is presented that automatically improves upon previous treatment plans by optimization under reference dose constraints. In such an optimization, a previous plan is taken as reference and a new optimization is performed towards some goal, such as minimization of the doses to healthy structures, under the constraint that no structure can become worse … Read more
Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact … Read more
This paper considers robust dynamic optimization problems, where the unknown parameters are modeled as uncertainty sets. We seek to bridge two classical paradigms for solving such problems, namely (1) Dynamic Programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We provide a set … Read more
This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a data-driven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X, the algorithm identifies a matrix C that … Read more
We study the convex hull of the intersection of a convex set E and a linear disjunction. This intersection is at the core of solution techniques for Mixed Integer Conic Optimization. We prove that if there exists a cone K (resp., a cylinder C) that has the same intersection with the boundary of the disjunction … Read more
The set of polynomials which are nonnegative over a subset of the nonnegative orthant (we call them set semidefinite) have many uses in optimization. A common example of this type of set is the set of copositive matrices, where effectively we are considering nonnegativity over the entire nonnegative orthant and we limit the polynomials to … Read more
We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such sparse approximate solutions using different greedy-type algorithms. … Read more
This paper is a follow up to the previous author’s paper on convex optimization. In that paper we began the process of adjusting greedy-type algorithms from nonlinear approximation for finding sparse solutions of convex optimization problems. We modified there three the most popular in nonlinear approximation in Banach spaces greedy algorithms — Weak Chebyshev Greedy … Read more
We present a capacity constrained network flow optimization approach for finding evacuation paths, flows and schedules so as to maximize the total evacuees for short notice evacuation planning (SNEP). Due to dynamic nature of this optimization problem, we first construct a timeexpanded network that expands the static network over the planning horizon for every time … Read more