相关论文: Sufficient optimality conditions in bilevel progra…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
This paper investigates the optimal control of a bilinear damped wave equation over an infinite time horizon. We establish the well-posedness of the controlled system and derive uniform energy estimates. The existence of optimal controls is…
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 article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
This paper proposes a new algorithm -- the \underline{S}ingle-timescale Do\underline{u}ble-momentum \underline{St}ochastic \underline{A}pprox\underline{i}matio\underline{n} (SUSTAIN) -- for tackling stochastic unconstrained bilevel…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel…
In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…
This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…
In this paper, we analyze optimal control problems governed by semilinear parabolic equations. Box constraints for the controls are imposed and the cost functional involves the state and possibly a sparsity-promoting term, but not a…
We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
We introduce an extended tangent cone of high order to a set and study its properties. Then we use this local approximation for deriving high-order necessary conditions for local minimizers of constrained optimization problems.
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…
Determinantal varieties -- the sets of bounded-rank matrices or tensors -- have attracted growing interest in low-rank optimization. The tangent cone to low-rank sets is widely studied and underpins a range of geometric methods. The…
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,…
The necessary conditions for an optimal control of a stochastic control problem with recursive utilities is investigated. The first order condition is the the well-known Pontryagin type maximum principle. When the optimal control satisfying…
This paper reviews gradient-based techniques to solve bilevel optimization problems. Bilevel optimization is a general way to frame the learning of systems that are implicitly defined through a quantity that they minimize. This…
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…
(Stochastic) bilevel optimization is a frequently encountered problem in machine learning with a wide range of applications such as meta-learning, hyper-parameter optimization, and reinforcement learning. Most of the existing studies on…