Implied constraints and LP duals of general nonlinear programming problems |
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| Institution: | 1. Lecturer, Gold Coast Campus, Southern Cross University, Bilinga, Queensland, Australia;2. Menzies Health Institute Queensland, Griffith University Gold Coast Campus, Queensland, Australia;3. Princess Alexandra Hospital, Woolloongabba, Queensland, Australia;4. Department of Emergency Medicine, Gold Coast University Hospital, Southport, Queensland, Australia;1. Faculty of Medicine, University of Novi Sad, Novi Sad, Serbia;2. Institute of Cardiovascular Diseases Vojvodina, Sremska Kamenica, Serbia;3. Department of Obstetrics and Gynecology, Clinical Center of Vojvodina, Serbia;1. Neuro-Intensive Care Unit, Fondation Rothschild, 29 rue Manin, 75019 Paris, France;2. Department of Neurology, Fondation Rothschild, 29 rue Manin, 75019 Paris, France;3. Intensive Care Unit, Department of Neurology, Pitié-Salpêtrière Hospital, Assistance Publique-Hôpitaux de Paris 47-85 Bd de l’Hôpital 75013 Paris, France |
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| Abstract: | A very surprising result is derived in this paper, that there exists a family of LP duals for general NLP problems. A general dual problem is first derived from implied constraints via a simple bounding technique. It is shown that the Lagrangian dual is a special case of this general dual and that other special cases turn out to be LP problems. The LP duals provide a very powerful computational device but are derived using fairly strict conditions. Hence, they can often be infeasible even if the primal NLP problem is feasible and bounded. Many directions for relaxing these conditions are outlined for future research. A concept of local duality is also introduced for the first time akin to the concept of local optimality. |
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