相关论文: Some remarks on the survey decimation algorithm fo…
How can we remove some interactions in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
We discuss the implementation of two distributed solvers of the random K-SAT problem, based on some development of the recently introduced survey-propagation (SP) algorithm. The first solver, called the "SP diffusion algorithm", diffuses as…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
We consider centralized and distributed mirror descent algorithms over a finite-dimensional Hilbert space, and prove that the problem variables converge to an optimizer of a possibly nonsmooth function when the step sizes are square…
Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the…
In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…
We consider the problem of minimizing a sum of $n$ functions over a convex parameter set $\mathcal{C} \subset \mathbb{R}^p$ where $n\gg p\gg 1$. In this regime, algorithms which utilize sub-sampling techniques are known to be effective. In…
In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…
The Survey Propagation (SP) algorithm for solving $k$-SAT problems has been shown recently as an instance of the Belief Propagation (BP) algorithm. In this paper, we show that for general constraint-satisfaction problems, SP may not be…
The convergence theory for the gradient sampling algorithm is extended to directionally Lipschitz functions. Although directionally Lipschitz functions are not necessarily locally Lipschitz, they are almost everywhere differentiable and…
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Submodularity is one of the most important property of combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of $k$-submodular function is NP-hard, and approximation algorithms are studied. For…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various…