Related papers: Self-accelerating root search and optimisation met…
Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…
Entropy regularized Markov decision processes have been widely used in reinforcement learning. This paper is concerned with the primal-dual formulation of the entropy regularized problems. Standard first-order methods suffer from slow…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
Functional iterations such as Newton's are a popular tool for polynomial root-finding. We consider realistic situation where some (e.g., better-conditioned) roots have already been approximated and where further computations is directed to…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
We present a study of several generic tree search techniques applied to the Sequential Ordering Problem. This study enables us to propose a simple and competitive tree search algorithm. It consists of an iterative Beam Search algorithm that…
In a recent paper, Bubeck, Lee, and Singh introduced a new first order method for minimizing smooth strongly convex functions. Their geometric descent algorithm, largely inspired by the ellipsoid method, enjoys the optimal linear rate of…
In this paper, applied strictly monotonic increasing scaled maps, a kind of well-conditioned linear barycentric rational interpolations are proposed to approximate functions of singularities at the origin, such as $x^\alpha$ for $\alpha \in…
We construct two optimal Newton-Secant like iterative methods for solving non-linear equations. The proposed classes have convergence order four and eight and cost only three and four function evaluations per iteration, respectively. These…
Many problems in machine learning and game theory can be formulated as saddle-point problems, for which various first-order methods have been developed and proven efficient in practice. Under the general convex-concave assumption, most…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…
Many popular first order algorithms for convex optimization, such as forward-backward splitting, Douglas-Rachford splitting, and the alternating direction method of multipliers (ADMM), can be formulated as averaged iteration of a…
A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) given in [20]. In this continuation paper, we introduce a…
We devise a simple but remarkably accurate iterative routine for calculating the roots of a polynomial of any degree. We demonstrate that our results have significant improvement in accuracy over those obtained by methods used in popular…
Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
First-order optimization methods are crucial for solving large-scale data processing problems, particularly those involving convex non-smooth composite objectives. For such problems with convex non-smooth composite objectives, we introduce…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…