Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in performing an iterative search for the shift akin to solving the secular equation in trust-region methods. Such search requires computing the Cholesky factorization of … Read more
We develop a trust-region method for minimizing the sum of a smooth term f and a nonsmooth term h, both of which can be nonconvex. Each iteration of our method minimizes apossibly nonconvex model of f+h in a trust region. The model coincides with f+h in value and subdifferential at the center. We establish global … Read more
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity and practical performance. The method contains elements of two existing methods: the classical gradient projection approach for bound-constrained optimization and a recently proposed Newton-conjugate gradient algorithm for unconstrained nonconvex optimization. Using a new definition of approximate … Read more
Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we … Read more
We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using Inexact Restoration-based adapted sample sizes. The sample size is chosen in an adaptive manner based on Inexact Restoration. The algorithm uses line search … Read more
In this paper, we present a first-order projection-free method, namely, the universal conditional gradient sliding (UCGS) method, for solving ε-approximate solutions to convex differentiable optimization problems. For objective functions with Hölder continuous gradients, we show that UCGS is able to terminate with ε-solutions with at most O((1/ε)^(2/(1+3v))) gradient evaluations and O((1/ε)^(4/(1+3v))) linear objective optimizations, where … Read more
This paper continues to address one of its author’s obsession with the well- known problem of dealing with non-convexity during the minimization of a nonlinear function f(x) by Newton-like methods. It builds on some proposals made by the present authors in “A Comparison of methods for traversing regions of non-convexity in optimization problems”. (Numerical Algorithms … Read more
In this paper, we solve the multiple product price optimization problem under interval uncertainties of the price sensitivity parameters in the demand function. The objective of the price optimization problem is to maximize the overall revenue of the firm where the decision variables are the prices of the products supplied by the firm. We propose … Read more
Optimizing the hyperparameters and architecture of a neural network is a long yet necessary phase in the development of any new application. This consuming process can benefit from the elaboration of strategies designed to quickly discard low quality configurations and focus on more promising candidates. This work aims at enhancing HyperNOMAD, a library that adapts … Read more
In this paper, we analyze the global convergence of a general non–monotone line search method on Riemannian manifolds. For this end, we introduce some properties for the tangent search directions that guarantee the convergence, to a stationary point, of this family of optimization methods under appropriate assumptions. A modified version of the non–monotone line search … Read more