Related papers: Global convergence and acceleration of projection …

In this paper, through a very intuitive vanilla proximal method perspective, we derive accelerated high-order optimization algorithms for minimizing a convex function that has H\"{o}lder continuous derivatives. In this general convex…

In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…

Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected…

We study distributed composite optimization over networks: agents minimize a sum of smooth (strongly) convex functions, the agents' sum-utility, plus a nonsmooth (extended-valued) convex one. We propose a general unified algorithmic…

For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…

We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…

In this paper, we consider the convex, finite-sum minimization problem with explicit convex constraints over strongly connected directed graphs. The constraint is an intersection of several convex sets each being known to only one node. To…

This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…

In this paper, we develop a new concept of Global Curvature Bound for an arbitrary nonlinear operator between abstract metric spaces. We use this notion to characterize the global complexity of high-order algorithms solving composite…

We present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time-varying connectivity. Our framework is general in that this value can represent a consensus…

In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…

The convergence of the generalized alternating projection (GAP) algorithm is studied in this paper to solve the compressive sensing problem $\yv = \Amat \xv + \epsilonv$. By assuming that $\Amat\Amat\ts$ is invertible, we prove that GAP…

Many descent algorithms for multiobjective optimization have been developed in the last two decades. Tanabe et al. (Comput Optim Appl 72(2):339--361, 2019) proposed a proximal gradient method for multiobjective optimization, which can solve…

This paper proposes a novel technique called "successive stochastic smoothing" that optimizes nonsmooth and discontinuous functions while considering various constraints. Our methodology enables local and global optimization, making it a…

This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…

We present a simple and efficient acceleration technique for an arbitrary method for computing the Euclidean projection of a point onto a convex polytope, defined as the convex hull of a finite number of points, in the case when the number…

This paper proposes a universal algorithm for convex minimization problems of the composite form $g_0(x)+h(g_1(x),\dots, g_m(x)) + u(x)$. We allow each $g_j$ to independently range from being nonsmooth Lipschitz to smooth, from convex to…

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…

This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…

Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which…