相关论文: A note on partial calmness for bilevel optimizatio…
The bilevel program is an optimization problem where the constraint involves solutions to a parametric optimization problem. It is well-known that the value function reformulation provides an equivalent single-level optimization problem but…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…
This paper is devoted to studying the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a…
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…
In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…
Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
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…
This paper studies the isolated calmness of the optimal solution mapping and the associated Lagrange system for regularized convex composite optimization problems. Several necessary and sufficient conditions for this property are…
Although the Karush-Kuhn-Tucker conditions suggest a connection between a conic optimization problem and a complementarity problem, it is difficult to find an accessible explicit form of this relationship in the literature. This note will…
We propose techniques for approximating bilevel optimization problems with non-smooth lower level problems that can have a non-unique solution. To this end, we substitute the expression of a minimizer of the lower level minimization problem…
Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…
Optimality conditions are central to analysis of optimization problems, characterizing necessary criteria for local minima. Formalizing the optimality conditions within the type-theory-based proof assistant Lean4 provides a precise, robust,…
We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation.…
Bilevel optimization reveals the inner structure of otherwise oblique optimization problems, such as hyperparameter tuning, neural architecture search, and meta-learning. A common goal in bilevel optimization is to minimize a…
This chapter presents a self-contained approach of variational analysis and generalized differentiation to deriving necessary optimality in problems of bilevel optimization with Lipschitzian data. We mainly concentrate on optimistic models,…
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…
Nonconvex-nonconcave minimax problems have found numerous applications in various fields including machine learning. However, questions remain about what is a good surrogate for local minimax optimum and how to characterize the minimax…
The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of stability analysis or bilevel optimization. An example of such a Lipschitzian property…