We propose a novel, optimization-based method that takes into account the objective and problem structure for reducing the number of scenarios, m, needed for solving two-stage stochastic optimization problems. We develop a corresponding convex optimization-based algorithm, and show that as the number of scenarios increase, the proposed method recovers the SAA solution. We report computational … Read more
Patient scheduling is a difficult task as it involves dealing with stochastic factors such as an unknown arrival flow of patients. Scheduling radiotherapy treatments for cancer patients faces a similar problem. Curative patients need to start their treatment within the recommended deadlines, i.e., 14 or 28 days after their admission while reserving treatment capacity for … Read more
It is widely accepted that the stepsize is of great significance to gradient method. Two efficient gradient methods with approximately optimal stepsizes mainly based on regularization models are proposed for unconstrained optimization. More exactly, if the objective function is not close to a quadratic function on the line segment between the current and latest iterates, … Read more
Centers of convex sets are geometric objects that have received extensive attention in the mathematical and optimization literature, both from a theoretical and practical standpoint. For instance, they serve as initialization points for many algorithms such as interior-point, hit-and-run, or cutting-planes methods. First, we observe that computing a Minkowski center of a convex set can be formulated as … Read more
Multistage mixed-integer distributionally robust optimization (DRO) forms a class of extremely challenging problems since their size grows exponentially with the number of stages. One way to model the uncertainty in multistage DRO is by creating sets of conditional distributions (the so-called conditional ambiguity sets) on a finite scenario tree and requiring that such distributions remain … Read more
In this paper, we look at the tool indexing problem in which a single copy of each tool is allowed in the tool magazine. We develop problem specific methods to search the neighborhood efficiently and design a Tabu Search algorithm based on them. Computational experiments show that our algorithm is competent. Citation Indian Institute of … Read more
The One-Dimensional Cutting Stock Problem with Setup Cost (CSP-S) is a cutting problem that seeks a cutting plan with a minimum number of objects and a minimum number of different patterns. This problem gains relevance in manufacturing settings, where time consuming operations to set up the knives of the cutting machine for the new patterns … Read more
Subgradient methods comprise a fundamental class of nonsmooth optimization algorithms. Classical results show that certain subgradient methods converge sublinearly for general Lipschitz convex functions and converge linearly for convex functions that grow sharply away from solutions. Recent work has moreover extended these results to certain nonconvex problems. In this work we seek to improve the … Read more
We propose an algorithm for computing the projection of a symmetric second-order tensor onto the cone of negative semidefinite symmetric tensors with respect to the inner product defined by an assigned positive definite symmetric fourth-order tensor C. The projection problem is written as a semidefinite programming problem and an algorithm based on a primal-dual path-following … Read more
Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform … Read more