LANGRANGE DUALITY FOR GENNERAL CONSTRAINED EXTREMUM PROBLEM
Keywords:General constrained extremum problem, Global minimum point, Sufficent optimality condition, Lagrange duality, Image set
The general constrained extremum problem is concerned in this paper for which the given cone with its interior being empty. Making use of the Lagrange duality theory with a class of regular weak separation functions in the image space, i.e., the space where the images of the objective and constraint functions run, a sufficient optimality condition for a global minimum point of that problem is presented. In addition, a state for a class of regular weak separation functions under an equivalence is also obtained. The result obtained in the literature is new and also illustrated by an example for our findings.
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