Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Stable barrier-projection and barrier-Newton methods in linear programming
Computational Optimization and Applications - Special issue dedicated to George Dantzig
A Preconditioned Conjugate Gradient Approach to Linear Equality Constrained Minimization
Computational Optimization and Applications
Tensor Methods for Equality Constrained Optimization
SIAM Journal on Optimization
Computing minimum distance between two implicit algebraic surfaces
Computer-Aided Design
| Hi-index | 0.00 |
This paper presents a unified gradient flow approach to nonlinear constrained optimization problems. This method is based on a continuous gradient flow reformulation of constrained optimization problems and on a two level time discretization of the gradient flow equation with a splitting parameter &thetas;. The convergence of the scheme is analyzed and it is shown that the scheme becomes first order when &thetas; ∈ [0, 1] and second order when &thetas; = 1 and the time discretization step length is sufficiently large. Numerical experiments for continuous, discrete and mixed discrete optimization problems were performed, and the numerical results show that the approach is effective for solving these problems.