Related papers: Convergence of a greedy algorithm for high-dimensi…
Boob et al. [1] described an iterative peeling algorithm called Greedy++ for the Densest Subgraph Problem (DSG) and conjectured that it converges to an optimum solution. Chekuri, Quanrud, and Torres [2] extended the algorithm to general…
We introduce a perturbed preconditioned gradient descent (PPGD) method for the unconstrained minimization of a strongly convex objective $G$ with a locally Lipschitz continuous gradient. We assume that $G(v)=E(v)+F(v)$ and that the gradient…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…
We prove convergence of a single time-scale stochastic subgradient method with subgradient averaging for constrained problems with a nonsmooth and nonconvex objective function having the property of generalized differentiability. As a tool…
We propose and analyze batch greedy heuristics for cardinality constrained maximization of non-submodular non-decreasing set functions. We consider the standard greedy paradigm, along with its distributed greedy and stochastic greedy…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of the…
We propose a variable decomposition algorithm -greedy block coordinate descent (GBCD)- in order to make dense Gaussian process regression practical for large scale problems. GBCD breaks a large scale optimization into a series of small…
Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
A multiscale optimization framework for problems over a space of Lipschitz continuous functions is developed. The method solves a coarse-grid discretization followed by linear interpolation to warm-start project gradient descent on…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
A framework is presented whereby a general convex conic optimization problem is transformed into an equivalent convex optimization problem whose only constraints are linear equations and whose objective function is Lipschitz continuous.…
The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this…
Recently, it has been discovered that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error being measured in the square norm. It was established that a simple greedy type…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
We introduce a notion of inexact model of a convex objective function, which allows for errors both in the function and in its gradient. For this situation, a gradient method with an adaptive adjustment of some parameters of the model is…
The proximal point algorithm, which is a well-known tool for finding minima of convex functions, is generalized from the classical Hilbert space framework into a nonlinear setting, namely, geodesic metric spaces of nonpositive curvature. We…
Subgradient methods comprise a fundamental class of nonsmooth optimization algorithms. Classical results show that certain subgradient methods converge sublinearly for general Lipschitz convex functions and converge linearly for convex…