Semidefinite programming (SDP) problems typically utilize the constraint that X-xx’ is PSD to obtain a convex relaxation of the condition X=xx’, where x is an n-vector. In this paper we consider a new hyperplane branching method for SDP based on using an eigenvector of X-xx’. This branching technique is related to previous work of Saxeena, … Read more
It is well known that the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around the point estimates of the expected asset returns. We investigate the performance of diagonal estimation-error matrices in the description of … Read more
In this paper, an inexact Alternating Direction Method of Multipliers (ADMM) has been proposed for solving the two-block separable convex optimization problem subject to linear equality constraints. The first resulting subproblem is solved inexactly under relative error criterion, while another subproblem called regularization problem is solved inexactly by introducing an indefinite proximal term. Meanwhile, the … Read more
The temporal bin packing problem with fire-ups (TBPP-FU) is a two-dimensional packing problem where one geometric dimension is replaced by a time horizon. The given items (jobs) are characterized by a resource consumption, that occurs exclusively during an activity interval, and they have to be placed on servers so that the capacity constraint is respected … Read more
Bilevel optimization is one of the fundamental problems in machine learning and optimization. Recent theoretical developments in bilevel optimization focus on finding the first-order stationary points for nonconvex-strongly-convex cases. In this paper, we analyze algorithms that can escape saddle points in nonconvex-strongly-convex bilevel optimization. Specifically, we show that the perturbed approximate implicit differentiation (AID) with … Read more
We propose a matheuristic approach to solve split delivery variants of the vehicle routing problem (VRP). The proposed method is based on the use of several mathematical programming components within an Iterated Local Search metaheuristic framework. In addition to well-known VRP local search heuristics, we include new types of improvement and perturbation strategies that are … Read more
CitationDepartment of Industrial Engineering, Middle East Technical University, Ankara, TurkeyArticleDownload View PDF
This paper addresses instances of the temporal fixed-charge multi-commodity flow (tfMCF) problem that arise in a very large scale dynamic transportation application. We model the tfMCF as a discrete-time Resource Task Network (RTN) with cyclic schedule, and formulate it as a mixed-integer program. These problems are notoriously hard to solve due to their time-expanded nature, … Read more
In this paper we propose an adaptive trust-region method for smooth unconstrained optimization. The update rule for the trust-region radius relies only on gradient evaluations. Assuming that the gradient of the objective function is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations required by the proposed method to generate approximate … Read more
We consider a real-world multimodal freight transportation problem that arises in a food grain organization in India. This problem aims to satisfy the demand for a set of warehouses for different types of food grains from another set of warehouses with surplus quantities over multiple periods of time by rail and road, while minimizing the … Read more