A squared‐variable transformation approach to nonlinear programming optimality conditions
Taylor, James G.
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We show that the well‐known necessary and sufficient conditions for a relative maximum of a nonlinear differentiable objective function with nonnegative variables constrained by nonlinear differentiable inequalities may be derived using the classical theory of equality constrained optimization problems with unrestricted variables. To do this we transform the original inequality‐constrained problem to an equivalent equality‐constrained problem by means of a well‐known squared‐variable transformation. Our major result is to show that second order conditions must be used to obtain the Kuhn‐Tucker conditions by this approach. Our nonlinear programming results are motivated by the development of some well‐known linear programming results by this approach.
The article of record as published may be found at http://dx.doi.org/10.1002/nav.3800200104
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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