We study a Stackelberg game in which a government positions rapid response teams and thereafter a terrorist attacks a location on a line segment. We assume the damage associated to such an attack to be time dependent. We show that there exists a subgame perfect Nash equilibrium that balances the possible damage on all intervals … Read more
Motivated by our collaboration with a residency program at an academic health system, we propose new integer programming (IP) approaches for the resident-to-rotation assignment problem (RRAP). Given sets of residents, resident classes, and departments, as well as a block structure for each class, staffing needs, rotation requirements for each class, program rules, and resident vacation … Read more
In this work, we present an algorithm for computing an enclosure for multi-objective mixed-integer nonconvex optimization problems. In contrast to existing solvers for this type of problem, this algorithm is not based on a branch-and-bound scheme but rather relies on a relax-and-refine approach. While this is an established technique in single-objective optimization, several adaptions to … Read more
We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum … Read more
In this paper, we propose a method that has foundations in the line search sequential quadratic programming paradigm for solving general nonlinear equality constrained optimization problems. The method employs a carefully designed modified line search strategy that utilizes second-order information of both the objective and constraint functions, as required, to mitigate the Maratos effect. Contrary … Read more
Crowdshipping, a rapidly growing approach in Last-Mile Delivery (LMD), relies on independent crowdworkers for delivery orders. Building a sustainable network of crowdshippers is essential for the survival and growth of such systems, while their participation is primarily motivated by fair pay. Additionally, the financial well-being of crowdworkers is sensitive to fair compensation, especially for those … Read more
In the minimum spanning tree (MST) interdiction problem, we are given a graph \(G=(V,E)\) with edge weights, and want to find some \(X\subseteq E\) satisfying a knapsack constraint such that the MST weight in \((V,E\setminus X)\) is maximized. Since MSTs of \(G\) are the minimum weight bases in the graphic matroid of \(G\), this problem … Read more
We analyze the inverse of the Gomory corner relaxation (GCR) of a pure integer program (IP). We prove the inverse GCR is equivalent to the inverse of a shortest path problem, yielding a polyhedral representation of the GCR inverse-feasible region. We present a linear programming (LP) formulation for solving the inverse GCR under the \(L_{1}\) … Read more
We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k-submodular function. We allow uncertainties arising from … Read more
We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP), in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the … Read more