Related papers: Generic property of the partial calmness condition…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…
This paper is concerned with the strong calmness of the KKT solution mapping for a class of canonically perturbed conic programming, which plays a central role in achieving fast convergence under situations when the Lagrange multiplier…
We provide sufficient conditions of local solvability for partial differential operators with variable Colombeau coefficients. We mainly concentrate on operators which admit a right generalized pseudodifferential parametrix and on operators…
In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…
When the lower-level optimal solution set-valued mapping of a bilevel optimization problem is not single-valued, we are faced with an ill-posed problem, which gives rise to the optimistic and pessimistic bilevel optimization problems, as…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
This paper presents a unified framework for investigating the partial condition number (CN) of the solution of double saddle point problems (DSPPs) and provides closed-form expressions for it. This unified framework encompasses the…
Using techniques of variational analysis, necessary and sufficient subdifferential conditions for H\"older error bounds are investigated and some new estimates for the corresponding modulus are obtained. As an application, we consider the…
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations…
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…
A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise…
In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establishing superlinear convergence rates of semismooth…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
A learning approach to selecting regularization parameters in multi-penalty Tikhonov regularization is investigated. It leads to a bilevel optimization problem, where the lower level problem is a Tikhonov regularized problem parameterized…
In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…
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…
We solve large-scale mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This is motivated by the MILPs being able to model problems in multi-agent autonomy, e.g., task assignment problems and…