  In this paper new descent line search iterative schemes for unconstrained as
well as constrained optimization problems are developed using q-derivative. At
every iteration of the scheme, a positive definite matrix is provided which is
neither exact Hessian of the objective function as in Newton scheme nor the
positive definite matrix as generated in quasi-Newton scheme. Second order
differentiablity property is not required in this process. Component of this
matrix are constructed using q-derivative of the function. It is proved that
the schemes preserve the property of Newton-like schemes in a local
neighborhood of a minimum point which leads to the super linear rate of
convergence. Numerical illustration of the scheme is also provided.
