Principles of Sequential Quadratic Programming Methods for Solving Nonlinear Programs

In this paper it is tried to describe to some extent the theoretical background and several practical aspects of sequential quadratic programming (S.QP) methods for solving the following standard problem $$\matrix{ {\left( {\rm{p}} \right)\min {\rm{f}}\left( {\rm{x}} \right)} \cr {{\rm{x}} \in {{\rm{R}}^{\rm{n}}}:{{\rm{g}}_{\rm{j}}}\left( {\rm{x}} \right) \le {\rm{0, j = 1,2, \ldots ,mi}}} \cr {{\rm{ }}{{\rm{g}}_{\rm{j}}}\left( {\rm{x}} \right) = {\rm{0, j = mi + 1, \ldots ,m,}}} \cr }$$ Where f,gj ∈ C2 (Rn).

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