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Quasi-Newton Methods
In this chapter we give a short introduction to Quasi-Newton methods (also known as variable metric methods or secant methods), which constitute an...
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Nonlinear Schwarz Preconditioning for Quasi-Newton Methods
In this work, we consider a nonlinear preconditioning strategy for Quasi-Newton (QN) methods. QN methods are a class of root-finding methods, where...
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Regularization of limited memory quasi-Newton methods for large-scale nonconvex minimization
This paper deals with regularized Newton methods, a flexible class of unconstrained optimization algorithms that is competitive with line search and...
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Quasi-Newton Methods
The idea of these methods is not to use the Hessian ∇2f(xk) of the minimizing function in the current point at every iteration, but instead to use an...
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Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization
We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from...
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An Overview of Stochastic Quasi-Newton Methods for Large-Scale Machine Learning
Numerous intriguing optimization problems arise as a result of the advancement of machine learning. The stochastic first-order method is the...
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Non-asymptotic superlinear convergence of standard quasi-Newton methods
In this paper, we study and prove the non-asymptotic superlinear convergence rate of the Broyden class of quasi-Newton algorithms which includes the...
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Memoryless Quasi-Newton Methods Based on the Spectral-Scaling Broyden Family for Riemannian Optimization
We consider iterative methods for unconstrained optimization on Riemannian manifolds. Though memoryless quasi-Newton methods are effective for...
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Polynomial worst-case iteration complexity of quasi-Newton primal-dual interior point algorithms for linear programming
Quasi-Newton methods are well known techniques for large-scale numerical optimization. They use an approximation of the Hessian in optimization...
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Two global quasi-Newton algorithms for solving matrix polynomial equations
In this article, we globalize the quasi-Newton algorithm proposed in Macías et al. (Appl Math Comput 441:127678, 2023) introducing an exact line...
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Quasi-Newton Single-Phase Stability Testing without Explicit Hessian Calculation
AbstractA robust algorithm (solver) for testing the single-phase stability of a multicomponent fluid under isochoric-isobaric conditions is...
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A limited memory Quasi-Newton approach for multi-objective optimization
In this paper, we deal with the class of unconstrained multi-objective optimization problems. In this setting we introduce, for the first time in the...
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A J-symmetric quasi-newton method for minimax problems
Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new...
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Proximal Quasi-Newton Method for Composite Optimization over the Stiefel Manifold
In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the...
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Modification of Quasi-Newton Successive Substitution Method for Calculating Phase Equilibria of Hydrocarbon Mixtures Taking into Account the Capillary Pressure Jump
AbstractA modification of the Quasi-Newton Successive Substitution method is presented, which is used to calculate phase equilibrium with a capillary...
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Correction of nonmonotone trust region algorithm based on a modified diagonal regularized quasi-Newton method
In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the...
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A modified secant equation quasi-Newton method for unconstrained optimization
One of the most prominent iterative approaches for solving unconstrained optimization problems is the quasi-Newton method. Their fast convergence and...
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A modified stochastic quasi-Newton algorithm for summing functions problem in machine learning
In this paper, a new stochastic quasi-Newton method (SQN) is proposed which has a different approximation of the Hessian inverse matrix
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A hybrid quasi-Newton method with application in sparse recovery
Imposing a rank-one modification on an adaptively scaled version of the identity matrix, we propose a memoryless symmetric rank-one quasi-Newton...
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A Study of a Posteriori Stop** in Iteratively Regularized Gauss–Newton-Type Methods for Approximating Quasi-Solutions of Irregular Operator Equations
AbstractA class of iteratively regularized Gauss–Newton-type methods for approximating quasi-solutions of irregular nonlinear operator equations in...