Solving Extremum and Critical Point Problems for Convex Functions
Newton's Method and Quadratic Interpolation Method Widely Used in Optimization Design for Solving Extremum and Critical Point Problems of Convex Functions
Application of Particle Swarm Optimization in Power Grid Reactive Power Optimization
Application of Particle Swarm Optimization in power grid reactive power optimization, primarily using the basic PSO algorithm combined with Newton's method for power flow calculation components
The Conjugate Gradient Method: Bridging Gradient Descent and Newton's Method
The Conjugate Gradient (CG) method serves as an intermediate approach between Steepest Descent and Newton's Method. It leverages only first-order derivative information while overcoming the slow convergence of Steepest Descent and avoiding the computational burden of storing, computing, and inverting the Hessian matrix required by Newton's Method. The CG method is not only one of the most useful techniques for solving large linear systems but also stands as one of the most efficient algorithms for large-scale nonlinear optimization problems. In implementation, CG typically uses iterative updates with conjugate directions computed through recurrence relations rather than matrix operations.
Optimization Algorithms
Optimization algorithms including Conjugate Gradient, Newton's Method, Golden Section Search, and Steepest Descent methods with implementation insights
Fundamental Algorithms in Optimization Methods
Implementation of key optimization algorithms: 1) Golden Section Method (0.618 Method), 2) Newton's Method, 3) Modified Newton's Method, 4) Fletcher-Reeves (FR) Method, 5) Davidon-Fletcher-Powell (DFP) Method
Various Numerical Optimization Algorithms
Comprehensive overview of numerical optimization algorithms including Newton's method, quasi-Newton methods, genetic algorithms, and more, with code implementation insights.
Optimization Theory Course Major Assignment: Implementation of Fundamental Optimization Algorithms
This source code package constitutes my major assignment for the Optimization Theory course, featuring self-implemented versions of the following prevalent optimization algorithms: Steepest Descent Method, Newton's Method, Nonlinear Least Squares Method, and DFP (Davidon-Fletcher-Powell) Method. The implementation includes two test functions, fun1 and fun2, designed to validate algorithm performance and convergence behavior across different optimization landscapes.
Newton-Raphson Method for Power Flow Calculation on IEEE 14-Bus System
A MATLAB-based implementation of Newton-Raphson method for power flow analysis on IEEE 14-bus test case, extendable to arbitrary power systems with nodal admittance matrix configuration
Finding a Root of Nonlinear Equations Using Fixed-Point Iteration Method
mulStablePoint - Finds a root of nonlinear equations using fixed-point iteration method; mulNewton - Uses Newton's method to find a root of nonlinear equations; mulDiscNewton - Applies discrete Newton's method to find a root of nonlinear equations; mulMix - Employs Newton-Jacobi iteration method to find a root of nonlinear equations; mulNewtonSOR - Utilizes Newton-SOR iteration method to find a root of nonlinear equations; mulDNewton - Implements Newton's descent method to find a root of nonlinear equations; mulGXF1 - Applies the first form of two-point secant method to find a root of nonlinear equations; mulGXF2 - Uses the second form of two-point secant method to find a root of nonlinear equations
Camera Calibration Toolbox
A classic and practical camera calibration toolbox authored by Caltech's Jean-Yves Bouguet, featuring nonlinear optimization techniques including Levenberg-Marquardt and Newton's methods for enhanced calibration accuracy.