相关论文: On the Nature of Regularity Assumptions in Bilevel…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by…
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…
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
Bilevel Optimization has experienced significant advancements recently with the introduction of new efficient algorithms. Mirroring the success in single-level optimization, stochastic gradient-based algorithms are widely used in bilevel…
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…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
Metric regularity is among the central concepts of nonlinear and variational analysis, constrained optimization, and their numerous applications. However, metric regularity can be elusive for some important ill-posed classes of problems…
We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning. In many practical cases, the upper and the lower objectives correspond to empirical risk…
We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the…
We study a class of bilevel optimization problems in which both the upper- and lower-level problems have minimax structures. This setting captures a broad range of emerging applications. Despite the extensive literature on bilevel…
This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a…
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…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
Bilevel optimization has found successful applications in various machine learning problems, including hyper-parameter optimization, data cleaning, and meta-learning. However, its huge computational cost presents a significant challenge for…
In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the…