\(\) A short, simple, and self-contained proof is presented showing that $n$-th lifting for the max-cut-polytope is exact. The proof re-derives the known observations that the max-cut-polytope is the projection of a higher-dimensional regular simplex and that this simplex coincides with the $n$-th semidefinite lifting. An extension to reduce the dimension of higher order liftings … Read more
The recently developed delayed weighted gradient method (DWGM) is competitive with the well-known conjugate gradient (CG) method for the minimization of strictly convex quadratic functions. As well as the CG method, DWGM has some key optimality and orthogonality properties that justify its practical performance. The main difference with the CG method is that, instead of … Read more
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
this paper, we study the single item capacitated multi-mode lot sizing problem with periodic carbon emission constraints where the carbon emission constraints define an upper bound for the average emission per product produced in any period. The uncapacitated version of this problem was introduced in Absi et al. (2013) and solved in polynomial time. We … 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 (DRO) with Sinkhorn distance—a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. Compared with Wasserstein DRO, our proposed approach offers enhanced computational tractability for a broader class of loss functions, and the worst-case distribution exhibits … 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
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
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