Alain Zemkoho

Stability analysis for two-level value functions and application to numerically solve a pessimistic bilevel program

  • Alain Zemkoho
    • Categories Bilevel Optimization Tags , , , ,

    Some stability results are presented for a two-level value function, which is the optimal value function of a parametric optimization problem constrained by the optimal solution set of another parameteric optimization problem. It is then shown how to use these stability results to write down (and subsequently compute) stationary points for a pessimistic bilevel optimization … Read more

    Mathematical programs with complementarity constraints and application to hyperparameter tuning for nonlinear support vector machines

  • Samuel Ward
  • Alain Zemkoho
  • Selin Damla Ahipasaoglu
    • Categories Bilevel Optimization, Complementarity and Variational Inequalities, Optimization in Data Science Tags , , , , ,

    We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard Constraint Qualifications (CQs). Carefully accounting for the combinatorial nature of the complementarity constraints, tractable versions of the Mangasarian Fromovitz Constraint Qualification (MFCQ) have been designed and widely studied in the literature. … Read more

    A new problem qualification based on approximate KKT conditions for Lipschitzian optimization with application to bilevel programming

  • Isabella Käming
  • Andreas Fischer
  • Alain Zemkoho
    • Categories Bilevel Optimization, Complementarity and Variational Inequalities, Nonsmooth Optimization

    When dealing with general Lipschitzian optimization problems, there are many problem classes where even weak constraint qualications fail at local minimizers. In contrast to a constraint qualification, a problem qualification does not only rely on the constraints but also on the objective function to guarantee that a local minimizer is a Karush-Kuhn-Tucker (KKT) point. For … Read more

    Relaxation methods for pessimistic bilevel optimization

  • Alain Zemkoho
    • Categories Bilevel Optimization, Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , , ,

    We consider a smooth pessimistic bilevel optimization problem, where the lower-level problem is convex and satisfies the Slater constraint qualification. These assumptions ensure that the Karush-Kuhn-Tucker (KKT) reformulation of our problem is well-defined. We then introduce and study the (i) Scholtes, (ii) Lin and Fukushima, (iii) Kadrani, Dussault and Benchakroun, (iv) Steffensen and Ulbrich, and … Read more

    Trajectory Optimization of Unmanned Aerial Vehicles in the Electromagnetic Environment

  • Alain Zemkoho
  • Jörg Fliege
    • Categories Control Applications, Nonlinear Optimization, Telecommunications

    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

  • Alain Zemkoho
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization

    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

  • Alain Zemkoho
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Optimization in Data Science Tags , , ,

    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

  • Yekini Shehu
  • Alain Zemkoho
  • Phan Tu Vuong
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , ,

    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

  • Stephan Dempe
  • Boris S. Mordukhovich
  • Alain Zemkoho
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    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

  • Alain Zemkoho
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    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