Farkas Lemmas and Lagrange Dualities for Composite Optimization Problems

doi:10.3969/j.cnki.jdxb.2015.06.003

Abstract

Abstract: Under the assumption that the functions are not necessarily continuous，by using the epigraph technique of conjugated functions，we introduce some new constraint qualifications，which completely characterize the Farkas lemma，the strong duality and the stable strong duality between the composite problem and its dual problem.Applications to the composite conical optimization problem are also given.

Key words: composite optimization, strong duality, Farkas lemma, composite conical optimization

GONG Xin, FANG Dong-Hui. Farkas Lemmas and Lagrange Dualities for Composite Optimization Problems[J]. journal6, 2015, 36(6): 8-13.

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