Related papers: Adaptive Proximal Method for Variational Inequalit…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…
We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator $F$ over a closed and convex set $S$. We assume that $S=C\cap A^{-1}(Q)$ is the nonempty solution set of a (multiple-set) split…
We show that adaptive proximal gradient methods for convex problems are not restricted to traditional Lipschitzian assumptions. Our analysis reveals that a class of linesearch-free methods is still convergent under mere local H\"older…
This paper considers a variational inequality (VI) problem arising from a game among multiple agents, where each agent aims to minimize its own cost function subject to its constrained set represented as the intersection of a (possibly…
We present a new adaptive collocation scheme for solving partial differential equations based on Local Coupled Multiquadrics (LCMQs) within a covers-and-nodes framework. The method, referred to as the Adaptive Ch Method, automatically…
We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…
This paper studies proximal gradient iterations for solving simple bilevel optimization problems where both the upper and the lower level cost functions are split as the sum of differentiable and (possibly nonsmooth) proximable functions.…
In this paper we present explicit estimate for Lipschitz constant of solution to a problem of calculus of variations. The approach we use is due to Gamkrelidze and is based on the equivalence of the problem of calculus of variations and a…
In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschitz continuous third-order derivatives. The methods are…
Many recently proposed gradient projection algorithms with inertial extrapolation step for solving quasi-variational inequalities in Hilbert spaces are proven to be strongly convergent with no linear rate given when the cost operator is…
The problem of individualized prediction can be addressed using variants of conformal prediction, obtaining the intervals to which the actual values of the variables of interest belong. Here we present a method based on detecting the…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
We propose an adaptive zeroth-order method for minimizing differentiable functions with $L$-Lipschitz continuous gradients. The method is designed to take advantage of the eventual compressibility of the gradient of the objective function,…
We propose a novel stochastic distributed method for both monotone and strongly monotone variational inequalities with Lipschitz operator and proper convex regularizers arising in various applications from game theory to adversarial…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…
We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…
We propose an approximation scheme for a class of semilinear variational inequalities whose Hamiltonian is convex and coercive. The proposed scheme is a natural extension of a previous splitting scheme proposed by Liang, Zariphopoulou and…