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The $O(1/k^2)$ convergence rate in function value of accelerated gradient descent is optimal, but there are many modifications that have been used to speed up convergence in practice. Among these modifications are restarts, that is,…
We consider stochastic variational inequalities with monotone operators defined as the expected value of a random operator. We assume the feasible set is the intersection of a large family of convex sets. We propose a method that combines…
We establish lower bounds on the complexity of finding $\epsilon$-stationary points of smooth, non-convex high-dimensional functions using first-order methods. We prove that deterministic first-order methods, even applied to arbitrarily…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
We present a simple transformation of any linear program or semidefinite program into an equivalent convex optimization problem whose only constraints are linear equations. The objective function is defined on the whole space, making…
In this paper, we are concerned with a worst-case complexity analysis of a-posteriori algorithms for unconstrained multiobjective optimization. Specifically, we propose an algorithmic framework that generates sets of points by means of…
A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding…
Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…
Partially observable Markov decision processes (POMDPs) have recently become popular among many AI researchers because they serve as a natural model for planning under uncertainty. Value iteration is a well-known algorithm for finding…
We propose an adaptive way to choose the anchoring parameters for the Halpern iteration to find a fixed point of a nonexpansive mapping in a real Hilbert space. We prove strong convergence of this adaptive Halpern iteration and obtain the…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
The problem of determining the (least) fixpoint of (higher-dimensional) functions over the non-negative reals frequently occurs when dealing with systems endowed with a quantitative semantics. We focus on the situation in which the…
Iteration methods based on barycentric rational interpolation are derived that exhibit accelerating orders of convergence. For univariate root search, the derivative-free methods approach quadratic convergence and the first-derivative…
Anderson acceleration (AA) is a technique for accelerating the convergence of fixed-point iterations. In this paper, we apply AA to a sequence of functions and modify the norm in its internal optimization problem to the $\mathcal{H}^{-s}$…
In this paper, we introduce the Adaptive Inertial Method (AIM), a novel framework for accelerated first-order methods through a customizable inertial term. We provide a rigorous convergence analysis establishing a global convergence rate of…
Algorithms for bilevel optimization often encounter Hessian computations, which are prohibitive in high dimensions. While recent works offer first-order methods for unconstrained bilevel problems, the constrained setting remains relatively…