The theory of optimal control is applied to obtain minimum-time trajectories for solar sail spacecraft for interplanetary missions. We consider the gravitational and solar radiation forces due to the Sun. The spacecraft is modelled as a flat sail of mass m and surface area A and is treated dynamically as a point mass. Coplanar circular orbits are assumed for the planets. We obtain optimal traje...

We propose a semismooth active-set Newton algorithm for solving the nonlinear complementarity problems with degenerate solutions. This method introduces the active-set technique to identify the degenerate set. At each iteration, the search direction is obtained by two reduced linear systems. Instead of employing gradient steps as adjustments to guarantee the sufficient reduction of the merit fu...

This paper deals with the e cient computation and bifurcation analysis of periodic solutions of large-scale dynamical systems, such as systems arising from the spatial discretization of partial di erential equations. The Newton-Picard method is an e cient single-shooting based technique based on a Newton-like linearization which exploits the low-dimensional dynamics observed in many systems. Th...

The multivariate eigenvalue problem (MEP) which originally arises from the canonical correlation analysis is an important generalization of the classical eigenvalue problem. Recently, the MEP also finds applications in many other areas and continues to receive interest. However, the existing algorithms for the MEP are the generalization of the power iteration for the classical eigenvalue proble...

This paper proposes an implementable proximal quasi-Newton method for minimizing a nondifferentiable convex function f in <n . The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point p(xk) of xk to define a vk ∈ ∂ k f(p(xk))with k ≤ α‖vk‖,where α is a constant. The method monitors the reduction in the value ...

We propose a procedure for building symmetric positive definite band preconditioners for large-scale symmetric, possibly indefinite, linear systems, when the coefficient matrix is not explicitly available, but matrix-vector products involving it can be computed. We focus on linear systems arising in Newton-type iterations within matrix-free versions of projected methods for bound-constrained no...

FACTS technology opens up new opportunity for operation and control of power system. Out of the various FACTS devices (viz-TCSC, TCPST, UPFC etc.), the right choices for the maximization of power flow in power system network demands attention which helps to achieve the active power flow up to their line limits without any constraint violation and with optimal investment on FACTS devices. In thi...

Training in the random neural network (RNN) is generally speci®ed as the minimization of an appropriate error function with respect to the parameters of the network (weights corresponding to positive and negative connections). We propose here a technique for error minimization that is based on the use of quasi-Newton optimization techniques. Such techniques o€er more sophisticated exploitation ...

Quasi-Newton methods have been utilized as a standard technique for solving nonlinear optimization problems and nonlinear systems of equations for over thirty years. These methods, in almost all cases, make use of data obtained from the step just completed in the variable space to revise the current approximation to the Hessian / Jacobian. Recently, a new class of multi-step quasi-Newton method...

The plain Newton-min algorithm to solve the linear complementarity problem (LCP for short) 0 ≤ x ⊥ (Mx + q) ≥ 0 can be viewed as a semismooth Newton algorithm without globalization technique to solve the system of piecewise linear equations min(x, Mx + q) = 0, which is equivalent to the LCP. When M is an M-matrix of order n, the algorithm is known to converge in at most n iterations. We show in...