Abstract
In this paper we propose a new family of curve search methods for unconstrained optimization problems, which are based on searching a new iterate along a curve through the current iterate at each iteration, while line search methods are based on finding a new iterate on a line starting from the current iterate at each iteration. The global convergence and linear convergence rate of these curve search methods are investigated under some mild conditions. Numerical results show that some curve search methods are stable and effective in solving some large scale minimization problems.
Highlights
Line search method is an important and mature technique in solving an unconstrained minimization problem min f ( x), x ∈ Rn, (1)where Rn is an n-dimensional Euclidean space and f : Rn → R1 is a continuously differentiable function
In this paper we present a new family of curve search methods for unconstrained minimization problems and prove their global convergence and linear convergence rate under some mild conditions
These method are based on searching a new iterate along a curve at each iteration, while line search methods are based on finding a new iterate on a line starting from the current iterate at each iteration
Summary
Line search method is an important and mature technique in solving an unconstrained minimization problem min f ( x), x ∈ Rn ,. It is required to solve some initial-value problems of ordinary differential equations to define the curves in ODE methods. In this paper we present a new family of curve search methods for unconstrained minimization problems and prove their global convergence and linear convergence rate under some mild conditions. These method are based on searching a new iterate along a curve at each iteration, while line search methods are based on finding a new iterate on a line starting from the current iterate at each iteration. Many curve search rules proposed in the paper can guarantee the global convergence and linear convergence rate of these curve search methods.
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