A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Trust region algorithms for optimization with nonlinear equality and inequality constraints
Trust region algorithms for optimization with nonlinear equality and inequality constraints
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
A trust region algorithm for equality constrained optimization
Mathematical Programming: Series A and B
On combining feasibility, descent and superlinear convergence in inequality constrained optimization
Mathematical Programming: Series A and B
Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Design and Testing of a Generalized Reduced Gradient Code for Nonlinear Programming
ACM Transactions on Mathematical Software (TOMS)
A Method for Computing All Solutions to Systems of Polynomials Equations
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.48 |
Feasible-points methods have several appealing advantages over the infeasible-points methods for solving equality-constrained nonlinear optimization problems. The known feasible-points methods however solve, often large, systems of nonlinear constraint equations in each step in order to maintain feasibility. Solving nonlinear equations in each step not only slows down the algorithms considerably, but also the large amount of floating-point computation involved introduces considerable numerical inaccuracy into the overall computation. As a result, the commercial software packages for equality-constrained optimization are slow and not numerically robust. We present a radically new approach to maintaining feasibility-called the canonical coordinates method (CCM). The CCM, unlike previous methods, does not adhere to the coordinate system used in the problem specification. Rather, as the algorithm progresses CCM dynamically chooses, in each step, a coordinate system that is most appropriate for describing the local geometry around the current iterate. By dynamically changing the coordinate system to suit the local geometry, the CCM is able to maintain feasibility in equality-constrained nonlinear optimization without having to solve systems of nonlinear equations. We describe the CCM and present a proof of its convergence. We also present a few numerical examples which show that CCM can solve, in very few iterations, problems that cannot be solved using the commercial NLP solver in MATLAB 6.1.