In this paper, we present a version of the Cubic Regularization of Newton’s method for unconstrained nonconvex optimization, in which the Hessian matrices are approximated by forward finite difference Hessians. The regularization parameter of the cubic models and the accuracy of the Hessian approximations are jointly adjusted using a nonmonotone line-search criterion. Assuming that the … Read more
We study multistage distributionally robust optimization (DRO) to hedge against ambiguity in quantifying the underlying uncertainty of a problem. Recognizing that not all the realizations and scenario paths might have an “effect” on the optimal value, we investigate the question of how to define and identify critical scenarios for nested multistage DRO problems. Our analysis … Read more
We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the rank minimization of a nonlinear feature map applied to the original matrix, which is then further approximated by … Read more
We study distributionally robust optimization with Sinkhorn distance—a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, … Read more
The uncertainty in infusion durations and non-homogeneous care level needs of patients are the critical factors that lead to difficulties in chemotherapy scheduling. We study the problem of scheduling patient appointments and assigning patients to nurses under uncertainty in infusion durations for a given day. We consider instantaneous nurse workload, represented in terms of total … Read more
This paper introduces a computational method for generating metric Travelling Salesperson Problem (TSP) instances having a large integrality gap. The method is based on the solution of an NP-hard problem, called IH-OPT, that takes in input a fractional solution of the Subtour Elimination Problem (SEP) on a TSP instance and compute a TSP instance having … Read more
In this paper, we present a novel scheduling problem, the stem cell culturing problem (SCP), which is identified in an attempt to improve the productivity of a manufacturing system producing a commercialized autologous stem cell therapeutic product for treating an incurable disease. For a given therapeutic product along with the corresponding manufacturing process, which is … Read more
Preference robust optimization (PRO) has recently been studied to deal with utility based decision making problems under ambiguity in the characterization of the decision maker’s (DM) preference. In this paper, we propose a novel PRO modeling paradigm which combines the stochastic utility theory with distributionally robust optimization technique. Based on the stochastic utility theory, our … Read more
Pareto efficiency for robust linear programs was introduced by Iancu and Trichakis. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with affine uncertainty. Additionally, we demonstrate the value of this approach in an exemplary manner in the area of robust semidefinite programming (SDP). In particular, we prove that computing … Read more
Intensity modulated radiation therapy (IMRT) is a widely used cancer treatment technique designed to target malignant cells. To enhance its effectiveness on tumors and reduce side effects, radiotherapy plans are usually divided into consecutive treatments, or fractions, that are delivered over multiple weeks. However, typical planning approaches have focused on finding the full sequence of … Read more