Univariate Search Method (Optimizing Quadratic Equations with Two Variables)

The algorithm summarizes the 1-dimensional search or univariate method

This method searches one dimension at a time thus optimizing only a single variable per iteration. As can be seen from the plot; the search begins from an initial guess i.e. (1,-5) in the example and achieves the minimum by optimizing the function in x and y dimensions intermittently till the net optimum is achieved. The intermittent optimization has been achieved by choosing the search direction vector as [1,0] and [0,1] for x and y coordinates respectively. The method is not completely accurate but the results obtained are satisfactory. One can change the convergence criteria for more accuracy.