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Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function
The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of...
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Rates of superlinear convergence for classical quasi-Newton methods
We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that...
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New Results on Superlinear Convergence of Classical Quasi-Newton Methods
We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result,...
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Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions
This study considers a proximal Newton-type method to solve the minimization of a composite function that is the sum of a smooth nonconvex function...
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A new semismooth Newton method for solving finite-dimensional quasi-variational inequalities
In this paper, we consider the numerical method for solving finite-dimensional quasi-variational inequalities with both equality and inequality...
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Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant condition
In this paper, we introduce a new variant of the BFGS method designed to perform well when gradient measurements are corrupted by noise. We show that...
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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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A stochastic extra-step quasi-Newton method for nonsmooth nonconvex optimization
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization...
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Methods for Large-Scale Optimization
In this chapter we present methods for solving large scale nonlinear equations and nonlinear unconstrained optimization problems. In particular, we...
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Greedy PSB methods with explicit superlinear convergence
Recently, Rodomanov and Nesterov proposed a class of greedy quasi-Newton methods and established the first explicit local superlinear convergence...
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A Quasi-Newton Method with Wolfe Line Searches for Multiobjective Optimization
We propose a BFGS method with Wolfe line searches for unconstrained multiobjective optimization problems. The algorithm is well defined even for...
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Continuous Projection Generalized Extra-Gradient Quasi-Newton Second-Order Method for Solving Saddle Point Problems
AbstractThe paper presents a study of a method for solving saddle point problems for convex-concave smooth functions with Lipschitz partial gradients...
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A hybrid semismooth quasi-Newton method for nonsmooth optimal control with PDEs
We propose a semismooth Newton-type method for nonsmooth optimal control problems. Its particular feature is the combination of a quasi-Newton method...
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A smoothing quasi-Newton method for solving general second-order cone complementarity problems
Recently, there are much interests in studying smoothing Newton method for solving montone second-order cone complementarity problem (SOCCP) or...
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SQP Methods
In this chapter we describe the essential features of the techniques known as Sequential Quadratic Programming (SQP) methods, which can be viewed as...
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Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints
We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale optimization with linear equality constraints. The methods are...
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A dense initialization for limited-memory quasi-Newton methods
We consider a family of dense initializations for limited-memory quasi-Newton methods. The proposed initialization exploits an...
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Numerical Methods of Optimization
The numerical methods of optimization start with optimizing functions of one variable, bisection, Fibonacci, and Newton. Then, functions of several...
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Quasi-Newton Methods
The Quasi-Newton methodsQuasi-Newton methods do not compute the Hessian of nonlinear functions. The Hessian is updated by analyzing successive...
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Inexact proximal DC Newton-type method for nonconvex composite functions
We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possibly...
