相关论文: Set-optimization meets variational inequalities

Algorithm selection is crucial in the field of optimization, as no single algorithm performs perfectly across all types of optimization problems. Finding the best algorithm among a given set of algorithms for a given problem requires a…

Many of the new developments in machine learning are connected with gradient-based optimization methods. Recently, these methods have been studied using a variational perspective. This has opened up the possibility of introducing…

The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or…

A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…

We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…

We provide new results of first-order necessary conditions of optimality problem in the form of John's theorem and in the form of Karush-Kuhn-Tucker's theorem. We establish our result in a topological vector space for problems with…

We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…

We consider a misspecified optimization problem that requires minimizing a function f(x;q*) over a closed and convex set X where q* is an unknown vector of parameters that may be learnt by a parallel learning process. In this context, We…

We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and…

In this paper, we focus on deriving some sufficient conditions for the existence of solutions to non-monotone Variational Inequalities (VIs) based on inverse mapping theory. We have obtained several widely applicable sufficient conditions…

Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that…

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…

Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to study the case of a multiobjective optimization problem…

In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by $L^1$-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic…

We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We extend the results in \cite{HJ15}, now in context of one-sided L\'evy risk models. We consider de…

Using the KKM technique, we establish some existence results for variational-hemivariational inequalities involving monotone set valued mappings on bounded, closed and convex subsets in reflexive Banach spaces. We also derive several…

We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…

We study optimality conditions for various types of control problems like the standard optimal control problem, optimal multiprocesses, problems with infinite horizon or the control of Volterra integral equations. To derive necessary…

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,…