Convex optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, proximal splitting algorithms are particularly adequate: they consist of simple operations, by handling the terms in the objective function separately. We present several existing proximal splitting algorithms and we derive new ones, within a unified framework, which consists … Read more
This study focuses on the development of a mixed binary primal-dual bilinear model for multi-period bilevel network expansion planning under uncertainty, where pricing-based equilibrated strategic and operational decisions are to be made. The periodwise dependent parameters’ uncertainty is represented by a _nite set of scenarios. Pricing-based equilibrium is required in the models to be optimized … Read more
A location-transportation problem concerns designing a company’s distribution network consisting of one central warehouse with ample stock and multiple local warehouses for a long but finite time horizon. The network is designed to satisfy the demands of geographically dispersed customers for multiple products within given delivery time targets. The company needs to first decide on … Read more
We present an approach to regularize and approximate solution mappings of parametric convex optimization problems that combines interior penalty (log-barrier) solutions with Tikhonov regularization. Because the regularized mappings are single-valued and smooth under reasonable conditions, they can be used to build a computationally practical smoothing for the associated optimal value function. The value function in … Read more
Maintaining an uninterrupted supply of electricity is a fundamental goal of power systems operators. However, due to critical outage events, customer demand or load is at times disconnected or shed temporarily. While deterministic optimization models have been devised to help operators expedite load shed recovery by harnessing the flexibility of the grid’s topology (i.e., transmission … Read more
The recent growth of direct-to-consumer deliveries has stressed the importance of last-mile logistics, becoming one of the critical factors in city planning. One of the key factors lies in the last-mile deliveries, reaching in some cases nearly 50% of the overall parcel delivery cost. Different variants of the the well-known Traveling Salesman Problem (TSP) arise … Read more
The Barzilai-Borwein (BB) gradient method is efficient for solving large-scale unconstrained problems to the modest accuracy and has a great advantage of being easily extended to solve a wide class of constrained optimization problems. In this paper, we propose a new stepsize to accelerate the BB method by requiring finite termination for minimizing two-dimensional strongly … Read more
In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal packing configurations are … Read more
Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work, we introduce an algorithm that removes units … Read more
Cutting planes accelerate branch-and-bound search primarily by cutting off fractional solutions of the linear programming (LP) relaxation, resulting in tighter bounds for pruning the search tree. Yet cutting planes can also reduce backtracking by excluding inconsistent partial assignments that occur in the course of branching. A partial assignment is inconsistent with a constraint set when … Read more