Abstract
Recent research has presented an extension from the traditional linear Lagrangian theory to nonlinear Lagrangian theory in order to achieve a guarantee of the identification of an optimal solution of the primal problem via dual search. This paper summarizes recent progress in new dual formulations with clear motivation and full geometric interpretation in order to better our understanding of the fundamental properties in constrained optimization and in the newly developed nonlinear Lagrangian duality theory.KeywordsNonlinear constrained optimizationglobal optimal solutionsaddle pointdual search p-th power formulationnonlinear Lagrangian
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