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A non-monotone trust-region method with noisy oracles and additional sampling
In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the...
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Proximal gradient algorithm with trust region scheme on Riemannian manifold
We consider the problem of minimizing the sum of a smooth function and nonsmooth function over a Riemannian manifold. We develop a Riemannian...
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Nonmonotone trust region algorithm for solving the unconstrained multiobjective optimization problems
In this work an iterative method to solve the nonlinear multiobjective problem is presented. The goal is to find locally optimal points for the...
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A Non-monotone Adaptive Scaled Gradient Projection Method for Orthogonality Constrained Problems
Optimization problems with orthogonality constraints are classical nonconvex nonlinear problems and have been widely applied in science and...
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An Active Set Trust-Region Method for Bound-Constrained Optimization
This paper discusses an active set trust-region algorithm for bound-constrained optimization problems. A sufficient descent condition is used as a...
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A New Nonmonotone Trust Region Barzilai-Borwein Method for Unconstrained Optimization Problems
In this paper, we propose a new nonmonotone trust region Barzilai-Borwein (BB for short) method for solving unconstrained optimization problems. The...
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A Multilevel Active-Set Trust-Region (MASTR) Method for Bound Constrained Minimization
Multilevel methods are known to be optimal solution strategies for systems arising from the discretization of, usually elliptic, PDEs, as their...
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Inexact restoration with subsampled trust-region methods for finite-sum minimization
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and...
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Two nonmonotone trust region algorithms based on an improved Newton method
In this paper, we present two improved regularized Newton methods for minimizing nonconvex functions with the trust region method. The fundamental...
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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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Nonmonotone Methods
In this chapter we introduce some globalization techniques for solving minimization problems and nonlinear equations, which relax the descent...
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An Inertial Spectral CG Projection Method Based on the Memoryless BFGS Update
Combining the derivative-free projection with inertial technique, we propose a hybrid inertial spectral conjugate gradient projection method for...
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Methods for Nonlinear Equations
In this chapter we consider solution methods for nonlinear equations, such as Newton type methods, Quasi-Newton methods and fixed point methods,...
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Effective matrix adaptation strategy for noisy derivative-free optimization
In this paper, we introduce a new effective matrix adaptation evolution strategy (
MADFO ) for noisy derivative-free optimization problems. Like everyMAES... 
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An inertial Fletcher–Reeves-type conjugate gradient projection-based method and its spectral extension for constrained nonlinear equations
In this paper, we initially enhance the Fletcher–Reeves (FR) conjugate parameter through a shrinkage multiplier, leading to a derivative-free...
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Newton’s Method
We report here some basic results on Newton-type methods. First we analyze local convergence properties of these methods in the solution of a system...
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A projection-based derivative free DFP approach for solving system of nonlinear convex constrained monotone equations with image restoration applications
The nonlinear programming makes use of quasi-Newton methods, a collection of optimization approaches when traditional Newton’s method are challenging...
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A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications
The conjugate gradient projection method (CGPM) has good theoretical properties and numerical performance for solving large-scale nonlinear monotone...
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The Boosted DC Algorithm for Linearly Constrained DC Programming
The Boosted Difference of Convex functions Algorithm (BDCA) has been recently introduced to accelerate the performance of the classical Difference of...
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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...
