Given a set of jobs (or items), each of which being characterized by its resource demand and its lifespan, and a sufficiently large number of identical servers (or bins), the busy time minimization problem (BTMP) requires to find a feasible schedule (i.e., a jobs-to-servers assignment) having minimum overall power-on time. Although being linked to the … Read more
We consider the problem of learning classification trees that are robust to distribution shifts between training and testing/deployment data. This problem arises frequently in high stakes settings such as public health and social work where data is often collected using self-reported surveys which are highly sensitive to e.g., the framing of the questions, the time … Read more
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The moment-SOS (sum of squares) hierarchy is a powerful approach for solving globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of increasing size, controlled by an integer, the relaxation order. We say that a relaxation of a given order is exact if … Read more
Vehicle routing problems (VRPs) with deadlines have received significant attention around the world. Motivated by a real-world food delivery problem, we assume that the travel time depends on the routing decisions, and study a data-driven stochastic VRP with deadlines and endogenous uncertainty. We use the non-parametric approaches, including k-nearest neighbor (kNN) and kernel density estimation … Read more
We propose a new approach based DC programming for fnding a solution of the partial facility interdiction problem that belongs to the class of bilevel programming. This model was frst considered in the work of Aksen et al. [1] with a heuristic algorithm named multi-start simplex search (MSS). However, because of the big number of … Read more
This paper focuses on solving mathematical programs with complementarity constraints (MPCCs) by assuming neither MPCC linear independence constraint qualification (MPCC-LICQ) nor lower/upper level strict complementarity at the solution. First, necessary conditions for MPCC local optimality and sufficient conditions for convergence to B-stationarity are investigated. Under MPCC-Abadie constraint qualification (MPCC-ACQ), we show that a local minimizer … Read more
In proton therapy treatment planning, the aim is to ensure tumor control while sparing the various surrounding risk structures. The biological effect of the irradiation depends on both physical dose and linear energy transfer (LET). In order to include LET alongside physical dose in plan creation, we propose to formulate the proton treatment planning problem … Read more
We consider a type of routing problems common in defence and security, in which we control a fleet of unmanned aerial vehicles (UAVs) that have to reach one or more target locations without being detected by an adversary. Detection can be carried out by a variety of sensors (radio receivers, cameras, personnel, etc) placed by … Read more
We consider bilevel programs where a single leader interacts with multiple followers who are coupled by a Nash equilibrium problem at the lower level. We generalize the value function reformulation to include multiple followers. This allows us to propose a convergent method based on the sequential convex approximation paradigm, and study the (exact or inexact) … Read more