Sequential quadratic programming (SQP) is used in solving nonlinear optimization problems, in a way that the basic problem is approximated by associated quadratic function, as well as the constrains of the initial problem. A mathematical model that has proven to be one of the best is Newton method, iterative method that tries to find solutions of the basic problem. In the first chapter we observe quadratic objective cost function \(f(x)=\frac{1}{2}x^{T}Ax-b^{T}x\) and its connection with unconstrained quadratic programming. Strictly convex quadratic functions has shown to be essential structure of unconstrained quadratic programming problem, because it guarantees the existence of extremes. In the second chapter we do the same analysis but with equality constrains, inequality constrains, and we have also observed case in which the constrains are specified with both equality and inequality constrains. Analyzing the problem, Lagrange function \(L_{0}\) has shown to be most useful tool because it issues of the initial objective function reduce to the analysis of the Lagrange function. Solvability of analysis, of the quadratic function problem, implemented in the first two chapters, we took as a prelude to analyze our problems of sequential quadratic programming, which we’ve shown in third chapter. Beside definitions, we have shown important theorems of convergency that justifies the application of Newton’s method.