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
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
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
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
Generation Capacity Expansion Planning (GCEP) requires high temporal resolution to account for the volatility of renewable energy supply. Because the GCEP optimization problem is often computationally intractable, time-series input data are often aggregated to representative periods using clustering. However, clustering removes extreme events, which are important to achieve reliable system designs. We present a method … 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 transportation problems and in many other planning problems, there are important sources of uncertainty that must be addressed to find effective and efficient solutions. A common approach for solving these dynamic and stochastic problems is the Multiple Scenario Approach (MSA), that has been proved effective for transportation problems, but it does not provide flexibility … Read more
In this technical report we present several Mixed Integer Linear Programming (MILP) models for the Berth Allocation and Quay Crane Assignment Problem (BACASP) considering crane movement and setup time (from now on: BACASP-S). First, we propose a MILP for the continuous-quay time-invariant BACASP in which both berthing time and position variables are continuous. Then, we … Read more
Cliques and their generalizations are frequently used to model “tightly knit” clusters in graphs and identifying such clusters is a popular technique used in graph-based data mining. One such model is the $s$-club, which is a vertex subset that induces a subgraph of diameter at most $s$. This model has found use in a variety … Read more