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Volume 2, Issue 3, 1 December 2018, Pages 317-342
Abstract. This paper presents a new Lagrange theory of discrete-continuous conic optimization in an infinite dimensional setting. The following questions are answered for discrete-continuous optimization problems: how to define a Lagrange functional, how Karush-Kuhn-Tucker conditions look like, and which duality results can be obtained? This approach is based on new separation theorems for discrete sets, which are also given in this paper. The developed theory is finally applied to problems of discrete-continuous semidefinite and copositive optimization.
How to Cite this Article:
Johannes Jahn, Martin Knossalla, Lagrange theory of discrete-continuous nonlinear optimization, J. Nonlinear Var. Anal. 2 (2018), 317-342.