Showing papers on "Nonlinear conjugate gradient method published in 1975"

Primer vector theory and applications

Abstract: A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed.

Pseudoinversus and conjugate gradients

Abstract: This paper is devoted to the study of connections between pseudoinverses of matrices and conjugate gradients and conjugate direction routines.

Parallel method of conjugate directions for minimization

Abstract: A nongradient method of conjugate directions for minimization id described. The method has the quadratic convergence property and is closely related to the method for linear systems, which makes it possible to use reduced algorithms when the corresponding matrix is sparse.

On the first conjugate point function for nonlinear differential equations

Abstract: Abstract We are concerned with the nth order differential equation y(n) = (x, y, y′, …,y(n-1)), where it is assumed throughout that f is continuous on [α,β) × Rn, α < β≤∞, and that solutions of initial value problems are unique and exist on [α, β). The definition of the first conjugate point function η1(t) for linear homogeneous equations is extended to this nonlinear case. Our main concern is what properties of this conjugacy function are valid in the nonlinear case.

On the Implementation of Reduced Gradient methods

Abstract: Until now, the implementation of reduced gradient methods had to be improvised empirically, since procedures for the truncation of the inner iterations, in the feasibility restoration stage, have not been analyzed with respect to convergence of the overall algorithm. This paper presents an implementation of one reduced gradient method. While retaining all the attractive features of the classical reduced gradient methods, this implementation incorporates, explicitly, efficient procedures for truncating the inner iterations to a finite number. In the paper, we present the properties of the restoration subalgorithm and we prove the convergence of the new algorithm under fairly general assumptions.

An alternate form of the conjugate gradient method for dynamic optimization

Abstract: The Polak-Ribiere conjugate gradient technique is here applied to a general optimal control problem. This method is a modification of the method of Lasdon, Mitter, and Waren. A convergence proof is presented.