Finding Solution of Nonlinear Constarined Optimization Using Spiral Optimization Algorithm

Abstract

A Nonlinear Constrained optimization is one of the interesting problems in optimization which arises frequently in a wide range of operational applications, scientific and engineering. The goal of this problem is solving an optimization problem where some of the constraints or the objective function are nonlinear. Some algorithms fail to find global solutions and focus only on local solutions. The augmented Lagrangian, sequential minimization method based on the use of penalty functions and interior-point methods, which are widely used, have advantage on their speed of convergence, but several important new challenges arise such as nonconvexity, the presence of nonlinearities and the need to ensure progress toward the solution. These methods are also assumed that the objective function is twice differentiability, for simple objective function it is easy to find the gradient and the hessian of the objective function but for complicated expression which is hard to find the derivative of the objective function analytically. In general, to satisfy optimality condition for nonlinearly constrained optimization, the differential form of the current objective function is required. In this paper, the proposed method is to find the global minimizer of general nonlinearly constrained optimization problems that its differential form is not needed.