Title: An Analysis of the Cauchy Method for Different Steplength Coefficient
Primary area: optimization
Keywords: SD method, steplenght, r value

Abstract: In this work we take the parameter r (recipprocal of optimal steplenth) as analysis target and introduce steplength coefficient t for classical steepest descent method for convex quadratic optimization problems, and we found the different coefficients affect the state of the entire system convergence. As the value of t varies, the overall system, including the value of r, may converge towards a fixed value, oscillate between two regions, or display chaotic behavior. We also conducted a specific analysis in the two-dimensional case.