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In this paper, we consider an unconstrained stochastic optimization problem where the objective function exhibits high-order smoothness. Specifically, we propose a new stochastic first-order method (SFOM) with multi-extrapolated momentum,…
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…
Discrete optimization is a central problem in mathematical optimization with a broad range of applications, among which binary optimization and sparse optimization are two common ones. However, these problems are NP-hard and thus difficult…
We consider information retrieval when the data, for instance multimedia, is coputationally expensive to fetch. Our approach uses "information filters" to considerably narrow the universe of possiblities before retrieval. We are especially…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
Sequential computation via autoregressive generation can make difficult tasks learnable, but the generation order of intermediate states strongly affects whether training succeeds. We address the problem of discovering a learning-friendly…
A parametric class of trust-region algorithms for unconstrained nonconvex optimization is considered where the value of the objective function is never computed. The class contains a deterministic version of the first-order Adagrad method…
We study ranked enumeration of join-query results according to very general orders defined by selective dioids. Our main contribution is a framework for ranked enumeration over a class of dynamic programming problems that generalizes…
Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time.…
Root-finding method is an iterative process that constructs a sequence converging to a solution of an equation. Householder's method is a higher-order method that requires higher order derivatives of the reciprocal of a function and has…
We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…
We present a new algorithm for refining a real interval containing a single real root: the new method combines characteristics of the classical Bisection algorithm and Newton's Iteration. Our method exhibits quadratic convergence when…
The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also the methods do not require…
In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen as a promising class of solution strategies, by forming…