Related papers: Proximal Flow Inspired Multi-Step Methods
Despite their frequent slow convergence, proximal gradient schemes are widely used in large-scale optimization tasks due to their tremendous stability, scalability, and ease of computation. In this paper, we develop and investigate a…
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.…
This paper proposes new proximal Newton-type methods with a diagonal metric for solving composite optimization problems whose objective function is the sum of a twice continuously differentiable function and a proper closed directionally…
In this work, we develop an accelerated sharp-interface method based on (Hu et al., JCP, 2006) and (Luo et al., JCP, 2015) for multiphase flows simulations. Traditional multiphase simulation methods use the minimum time step of all fluids…
We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal-Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in…
This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function…
In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…
The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…
The proximal gradient descent method, well-known for composite optimization, can be completely described by the concept of proximal gradient mapping. In this paper, we highlight our previous two discoveries of proximal gradient…
In the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties.…
We propose and analyze asymptotic proximal point (APP) methods to find the global minimizer for a class of nonconvex, nonsmooth, or even discontinuous multiple minima functions. The method is based on an asymptotic representation of…
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure…
This paper presents a comprehensive analysis of a broad range of variations of the stochastic proximal point method (SPPM). Proximal point methods have attracted considerable interest owing to their numerical stability and robustness…
Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
This report presents a low computational and cognitive complexity, stable, time accurate and adaptive method for the Navier-Stokes equations. The improved method requires a minimally intrusive modification to an existing program based on…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…