Related papers: Adaptive Approximation for Multivariate Linear Pro…
This work studies a class of non-smooth decentralized multi-agent optimization problems where the agents aim at minimizing a sum of local strongly-convex smooth components plus a common non-smooth term. We propose a general primal-dual…
In this two-part work, we propose an algorithmic framework for solving non-convex problems whose objective function is the sum of a number of smooth component functions plus a convex (possibly non-smooth) or/and smooth (possibly non-convex)…
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution…
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…
In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Motivated by some applications in signal processing and machine learning, we consider two convex optimization problems where, given a cone $K$, a norm $\|\cdot\|$ and a smooth convex function $f$, we want either 1) to minimize the norm over…
A convex optimization model predicts an output from an input by solving a convex optimization problem. The class of convex optimization models is large, and includes as special cases many well-known models like linear and logistic…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When…
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
Linear models have shown great effectiveness and flexibility in many fields such as machine learning, signal processing and statistics. They can represent rich spaces of functions while preserving the convexity of the optimization problems…
In this paper, we study a class of bilevel programming problem where the inner objective function is strongly convex. More specifically, under some mile assumptions on the partial derivatives of both inner and outer objective functions, we…
While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this paper, we describe an…
A rational approximation by a ratio of polynomial functions is a flexible alternative to polynomial approximation. In particular, rational functions exhibit accurate estimations to nonsmooth and non- Lipschitz functions, where polynomial…
We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…