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We consider the gradient method with variable step size for minimizing functions that are definable in o-minimal structures on the real field and differentiable with locally Lipschitz gradients. We prove that global convergence holds if…
We consider the minimization of a cost function $f$ on a manifold $M$ using Riemannian gradient descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality conditions within a tolerance $\varepsilon$.…
We propose a projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization, where the objective function is a nested composition of $T$ functions and the constraint set is a closed convex…
We investigate the implementation of a new stochastic Kuramoto-Vicsek-type model for global optimization of nonconvex functions on the sphere. This model belongs to the class of Consensus-Based Optimization. In fact, particles move on the…
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
A new universal derivative-free optimization method CDOS (Conjugate Direction with Orthogonal Shift) is proposed. The CDOS method was specially developed to solve optimization tasks where the objective function and constraints are black…
We propose a regularized Hessian-free Newton-type method for minimizing smooth convex functions with Lipschitz continuous Hessians. The algorithm constructs an approximate Hessian by finite differences and selects the regularization…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a…
We propose a new discrete FFT-based method for computational homogenization of micromechanics on a regular grid that is simple, fast and robust. The discretization scheme is based on a tetrahedral stencil that displays three crucial…
In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for…
This paper is concerned with multi-agent optimization problem. A distributed randomized gradient-free mirror descent (DRGFMD) method is developed by introducing a randomized gradient-free oracle in the mirror descent scheme where the…
The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…
Global optimization of a non-convex objective function often appears in large-scale machine-learning and artificial intelligence applications. Recently, consensus-based optimization (in short CBO) methods have been introduced as one of the…
We present an intriguing discovery related to Random Fourier Features: in Gaussian kernel approximation, replacing the random Gaussian matrix by a properly scaled random orthogonal matrix significantly decreases kernel approximation error.…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
In this paper, we introduce some new iterative optimisation algorithms on Riemannian manifolds and Hilbert spaces which have good global convergence guarantees to local minima. More precisely, these algorithms have the following properties:…
In this paper we consider the unconstrained minimization problem of a smooth function in ${\mathbb{R}}^n$ in a setting where only function evaluations are possible. We design a novel randomized derivative-free algorithm --- the stochastic…
We introduce a derivative-free global optimization algorithm that efficiently computes minima for various classes of one-dimensional functions, including non-convex, and non-smooth functions.This algorithm numerically approximates the…