Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes bipartite graph matching and graph partitioning as special cases and is NP-hard, in general. We develop scalable linear … Read more
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is meant for a point to approximately solve the constraints, determining bounds on the expected number of iterations reduces to … Read more
Nonsmooth optimization problems arising in practice, whether in signal processing, statistical estimation, or modern machine learning, tend to exhibit beneficial smooth substructure: their domains stratify into “active manifolds” of smooth variation, which common proximal algorithms “identify” in finite time. Identification then entails a transition to smooth dynamics, and permits the use of second-order information for … Read more
We study a variant of the Probabilistic Travelling Salesman Problem arising when retailers crowdsource last-mile deliveries to their own customers, who can refuse or accept in exchange for a reward. A planner must identify which deliveries to offer, knowing that all deliveries need fulfilment, either via crowdsourcing or using the retailer’s own vehicle. We formalise … Read more
This work presents a general method for linearizing bilinear terms in the upper level of bilevel optimization problems when the bilinear terms are products of the primal and dual variables of the lower level. Bilinear terms of this form often appear in energy market optimization models where the dual variable represents the market price of … Read more
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. This new method is then extended to solve a general multi-block separable convex optimization problem, and two related primal-dual hybrid gradient algorithms are also discussed. … Read more
Network segmentation of a power grid’s communication system is one way to make the grid more resilient to cyber attacks. We develop a novel trilevel programming model to optimally segment a grid communication system, taking into account the actions of an information technolology (IT) administrator, attacker, and grid operator. The IT administrator is given an … Read more
We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensitymodulated particle therapy (IMPT) treatment planning. Proton therapy necessitates a high level of delivery accuracy to exploit the selective targeting imparted by the Bragg peak. For this purpose, pCT utilizes the proton beam itself … Read more
This paper studies optimal criteria for the appointment scheduling of outpatients in a medical imaging center. The main goal of this study is to coordinate the assignments of radiopharmaceuticals and the scheduling of outpatients on imaging scanners. We study a special case of a molecular imaging center that offers services for various diagnostic procedures for … Read more
In this paper, we address the Minimization of Open Stacks Problem (MOSP). This problem often appears during production planning of manufacturing industries, such as in the cutting of objects to comply with space constraints around the cutting machine in the glass, furniture, and metallurgical industries. The MOSP is also pertinent to the field of VLSI … Read more