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This paper is devoted to the analysis of worst case complexity bounds for linesearch-type derivative-free algorithms for the minimization of general non-convex smooth functions. We consider a derivative-free algorithm based on a linesearch ...$$$\mathcal{}{}^{\mathrm{}}$$$$\mathcal{}{}^{\mathrm{}}$

In this paper, we propose a derivative-free Levenberg-Marquardt algorithm for nonlinear least squares problems, where the Jacobian matrices are approximated via orthogonal spherical smoothing. It is shown that the gradient models which use the ...

The Barzilai–Borwein (BB) method is a popular and efficient gradient method for solving large-scale unconstrained optimization problems. In general, it converges much faster than the steepest descent (Cauchy) method. However, it may not converge, ...

In this paper, a hybrid three-term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is computed such that it is close to the direction obtained by the memoryless Broyden–...

The problem of finding a globally optimal k-partition of a set $\mathcal{A}$ is a very intricate optimization problem for which in general, except in the case of one-dimensional data, i.e., for data with one feature ($\mathcal{A}\subset \mathbb{R}$), there is no method to solve. Only in ...$\mathcal{}{\mathbb{}}^{}$$\mathrm{}$

This note provides a counterexample to a theorem announced in the last part of the paper (Vicente and Custódio Math Program 133:299–325, 2012). The counterexample involves an objective function $f:\mathbb{R}\to \mathbb{R}$ which satisfies all the assumptions required by ...${{}_{}}_{\mathbb{}}$${}_{}$${}_{}$${}_{}{}_{}$${}_{}$

We consider the oracle complexity of computing an approximate stationary point of a Lipschitz function. When the function is smooth, it is well known that the simple deterministic gradient method has finite dimension-free oracle complexity. ...

Many practical problems involve the optimization of computationally expensive blackbox functions. The computational cost resulting from expensive function evaluations considerably limits the number of true objective function evaluations allowed in ...

In this paper, we propose an adaptation of the well-known k-means algorithm for solving the multiple spheres detection problem when data points are homogeneously scattered around several spheres. We call this adaptation the k-closest spheres ...

• Efficient novel algorithm for solving the multiple spheres detection problem.
• k-Closest spheres algorithm based on the k-means algorithm.
• Initial spheres are determined using a few iterations of the DIRECT algorithm.

In this paper, we propose a method for efficiently obtaining an approximate solution for constrained nonlinear monotone operator equations. The search direction of the proposed method closely aligns with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) ...

In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated via scalarization using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus ...

In this paper, we present convergence guarantees for a modified trust-region method designed for minimizing objective functions whose value and gradient and Hessian estimates are computed with noise. These estimates are produced by generic ...

In this paper, we propose a projection-based hybrid spectral gradient algorithm for nonlinear equations with convex constraints, which is based on a certain line search strategy. Convex combination technique is used to design a novel spectral ...

In this paper, we propose a new modification of a three-term derivative-free projection algorithm for solving a system of monotone nonlinear equations. The global convergence was proved under some suitable conditions, and the search direction of ...

Combining the derivative-free projection with inertial technique, we propose a hybrid inertial spectral conjugate gradient projection method for solving constrained nonlinear monotone equations. The conjugate parameter is a hybrid modification ...

In this work, we propose a free derivative quasi-Newton method for solving large-scale nonlinear systems of equation. We introduce a two-stage linear search direction and develop its global convergence theory. Besides, we prove that the method ...

In this paper we provide a rigorous convergence analysis for the renowned particle swarm optimization method by using tools from stochastic calculus and the analysis of partial differential equations. Based on a continuous-time formulation of the ...

Al-Baali et al. (Comput. Optim. Appl. 60:89–110, 2015) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition and global convergence. In this paper, we extend this method to a family of three-term ...

This paper presents a new sufficiently descent algorithm for system of nonlinear equations where the underlying operator is pseudomonotone. The conditions imposed on the proposed algorithm to achieve convergence are Lipschitz continuity and ...

Quantum computing has entered its mature life thanks to the availability of cloud-based Noisy Intermediate-Scale Quantum (NISQ) technologies. These devices allow quantum researchers and practitioners to design, develop and test quantum ...

• Quantum computing has entered its mature life thanks to NISQ technologies.
• NISQ ...