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In this paper, we study the non-monotone adaptive submodular maximization problem subject to a cardinality constraint. We first revisit the adaptive random greedy algorithm proposed in \citep{gotovos2015non}, where they show that this…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
We propose an optimization proxy in terms of iterative implicit gradient methods for solving constrained optimization problems with nonconvex loss functions. This framework can be applied to a broad range of machine learning settings,…
Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…
In this paper, we propose a subgradient algorithm with a non-asymptotic convergence guarantee to solve copositive programming problems. The subproblem to be solved at each iteration is a standard quadratic programming problem, which is…
We propose a novel continuous-time algorithm for inequality-constrained convex optimization inspired by proportional-integral control. Unlike the popular primal-dual gradient dynamics, our method includes a proportional term to control the…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called \emph{weak Minty} solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of…
It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint…
In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…
In this paper, we propose a quasi-Newton method for solving smooth and monotone nonlinear equations, including unconstrained minimization and minimax optimization as special cases. For the strongly monotone setting, we establish two global…
In this paper, we consider a broad class of nonconvex and nonsmooth optimization problems, where one objective component is a nonsmooth weakly convex function composed with a linear operator. By integrating variable smoothing techniques…
The bilevel variational inequality (BVI) problem is a general model that captures various optimization problems, including VI-constrained optimization and equilibrium problems with equilibrium constraints (EPECs). This paper introduces a…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from…
The compact Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. It is further developed to be more flexible in solving the…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most $n$ components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence…
We study first-order methods for constrained min-max optimization. Existing methods either require two gradient calls or two projections in each iteration, which may be costly in some applications. In this paper, we first show that a…
We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…