Related papers: Variational and quasi-variational inequalities und…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
The class PLS (Polynomial Local Search) captures the complexity of finding a solution that is locally optimal and has proven to be an important concept in the theory of local search. It has been shown that local search versions of various…
This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method…
We use the concept of barrier-based smoothing approximations introduced in [ C. B. Chua and Z. Li, A barrier-based smoothing proximal point algorithm for NCPs over closed convex cones, SIOPT 23(2), 2010] to extend the non-interior…
The standard mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex are based on proper discrete subcomplexes. As a consequence, the exterior derivatives, which are local operators, are computed…
In this paper, we study the application of quasi-Newton methods for solving empirical risk minimization (ERM) problems defined over a large dataset. Traditional deterministic and stochastic quasi-Newton methods can be executed to solve such…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…
This paper is concerned with the variational inequality problem (VIP) over the fixed point set of a quasi-nonexpansive operator. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen…
Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional differentiability and optimal control of such QVIs. We give three existence theorems based…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
We focus on three different convexity principles for local and nonlocal variational integrals. We prove various generalizations of them, as well as their equivalences. Some applications to nonlinear eigenvalue problems and Hardy-type…
The paper introduces and characterizes new notions of Lipschitzian and H\"olderian full stability of solutions to general parametric variational systems described via partial subdifferential and normal cone mappings acting in Hilbert…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…