Trajectory Optimization of Unmanned Aerial Vehicles in the Electromagnetic Environment

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

Bilevel Hyperparameter Optimization for Nonlinear Support Vector Machines

While the problem of tuning the hyperparameters of a support vector machine (SVM) via cross-validation is easily understood as a bilevel optimization problem, so far, the corresponding literature has mainly focused on the linear-kernel case. In this paper, we establish a theoretical framework for the development of bilevel optimization-based methods for tuning the hyperparameters of … Read more

Deep learning and hyperparameter optimization for assessing one’s eligibility for a subcutaneous implantable cardioverter-defibrillator

In cardiology, it is standard for patients suffering from ventricular arrhythmias (the leading cause of sudden cardiac death) belonging to high risk populations to be treated using Subcutaneous Implantable Cardioverter-Defibrillators (S-ICDs). S-ICDs carry a risk of so-called T Wave Over Sensing (TWOS), which can lead to inappropriate shocks with an inherent health risk. For this … Read more

An inertial extrapolation method for convex simple bilevel optimization

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and nonsmooth functions while the outer one is the minimization … Read more

Two-level value function approach to nonsmooth optimistic and pessimistic bilevel programs

The authors’ paper in Ref. [5], was the first one to provide detailed optimality conditions for pessimistic bilevel optimization. The results there were based on the concept of the two-level optimal value function introduced and analyzed in Ref. [4], for the case of optimistic bilevel programs. One of the basic assumptions in both of these … Read more

Estimates of generalized Hessians for optimal value functions in mathematical programming

The \emph{optimal value function} is one of the basic objects in the field of mathematical optimization, as it allows the evaluation of the variations in the \emph{cost/revenue} generated while \emph{minimizing/maximizing} a given function under some constraints. In the context of stability/sensitivity analysis, a large number of publications have been dedicated to the study of continuity … Read more

Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to … Read more

KKT Reformulation and Necessary Conditions for Optimality in Nonsmooth Bilevel Optimization

For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question. Recently though, this widespread believe was shown to be false in general. In this paper, other aspects of the difference between both … Read more

Necessary optimality conditions in pessimistic bilevel programming

This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipschitz continuity of … Read more

Sensitivity analysis for two-level value functions with applications to bilevel programming

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more dicult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary … Read more