Related papers: Second-order optimality conditions for bilevel pro…
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…
Some classic second-order sufficient optimality conditions in the calculus of variations are shown to be equivalent, while also introducing a new equivalent second-order condition which is extremely easy to apply: simply integrate a linear…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
This paper focuses on optimality conditions for $C^{1,1}$-smooth optimization problems subject to inequality and equality constraints. By employing the concept of limiting (Mordukhovich) second-order subdifferentials to the Lagrangian…
For bilevel programs with a convex lower level program, the classical approach replaces the lower level program with its Karush-Kuhn-Tucker condition and solve the resulting mathematical program with complementarity constraint (MPCC). It is…
We investigate a family of bilevel imaging learning problems where the lower-level instance corresponds to a convex variational model involving first- and second-order nonsmooth sparsity-based regularizers. By using geometric properties of…
This paper presents a comprehensive review of techniques proposed in the literature for solving bilevel optimization problems encountered in various real-life applications. Bilevel optimization is an appropriate choice for hierarchical…
In this paper we propose a bilevel optimization approach for the placement of space and time observations in variational data assimilation problems. Within the framework of supervised learning, we consider a bilevel problem where the…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
In this article we study optimal control problems for systems that are affine with respect to some of the control variables and nonlinear in relation to the others. We consider finitely many equality and inequality constraints on the…
In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…
Bilevel linear programming (LP) is one of the simplest classes of bilevel optimization problems, yet it is known to be NP-hard in general. Specifically, determining whether the optimal objective value of a bilevel LP is at least as good as…
In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…
Bilevel programs model sequential decision interactions between two sets of players and find wide applications in real-world complex systems. In this paper, we consider a bilevel mixed-integer linear program with binary tender, wherein the…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…
In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…
In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some second-order constraint…