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We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling…

Optimization and Control · Mathematics 2021-09-28 Raghu Bollapragada , Stefan M. Wild

An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…

Optimization and Control · Mathematics 2019-01-11 Alexander I. Golikov , Igor E. Kaporin

We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…

Optimization and Control · Mathematics 2021-02-25 Coralia Cartis , Lindon Roberts

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

Methodology · Statistics 2019-01-21 Filip Tronarp , Simo Särkkä

Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiserobtained using these iterative…

Numerical Analysis · Mathematics 2020-04-07 Yasunori Aoki , Ken Hayami , Kota Toshimoto , Yuichi Sugiyama

This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…

Optimization and Control · Mathematics 2021-05-04 Nikita Yudin , Alexander Gasnikov

This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…

Numerical Analysis · Mathematics 2025-11-10 Fleurianne Bertrand , Maximilian Brodbeck , Tim Ricken , Henrik Schneider

We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…

Optimization and Control · Mathematics 2024-09-04 Matt Menickelly , Stefan M. Wild , Miaolan Xie

In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss-Newton algorithm, and as such do not require…

Numerical Analysis · Mathematics 2025-06-13 Alban Bloor Riley , Marcus Webb , Michael L Baker

We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…

Statistical Mechanics · Physics 2015-05-18 Luis F. Lafuerza , Raul Toral

Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…

Optimization and Control · Mathematics 2019-01-25 Ching-pei Lee , Stephen J. Wright

We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the…

Optimization and Control · Mathematics 2019-05-15 Peng Xu , Fred Roosta , Michael W. Mahoney

A practical challenge for structural estimation is the requirement to accurately minimize a sample objective function which is often non-smooth, non-convex, or both. This paper proposes a simple algorithm designed to find accurate solutions…

Econometrics · Economics 2025-08-19 Jean-Jacques Forneron

In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…

Optimization and Control · Mathematics 2019-10-22 Minghan Yang , Andre Milzarek , Zaiwen Wen , Tong Zhang

This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost…

Optimization and Control · Mathematics 2014-10-17 Stefan Streif , Matthias Karl , Ali Mesbah

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

Optimization and Control · Mathematics 2021-07-08 Morteza Boroun , Afrooz Jalilzadeh

The Gauss-Newton's method for solving nonlinear least squares problems is studied in this paper. Under the hypothesis that the derivative of the function associated with the least square problem satisfies a majorant condition, a local…

Optimization and Control · Mathematics 2010-03-29 O. P. Ferreira , M. L. N. Goncalves , P. R. Oliveira

We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…

Optimization and Control · Mathematics 2019-10-31 Raghu Bollapragada , Stefan M. Wild

Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…

Optimization and Control · Mathematics 2020-02-06 Aliyu Muhammed Awwal , Poom Kumam , Hassan Mohammad

Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…

Machine Learning · Statistics 2021-11-04 Andrés F. López-Lopera , François Bachoc , Nicolas Durrande , Olivier Roustant