Continuation method for nonlinear complementarity problems via normal maps |
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| Institution: | 1. Department of Management and Decision Sciences, College of Business and Economics, Washington State University, Pullman, WA 99164-4736, USA;2. Department of Operations and Information Management, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA;3. Department of Industrial Engineering, Faculty of Engineering, 06533 Bilkent, Ankara, Turkey;1. Ass. EURATOM/ENEA/CREATE, Universita’ di Napoli “Federico II”, Naples, Italy;2. Ass. EURATOM/ENEA/CREATE, Universita’ di Napoli “Parthenope”, Naples, Italy;3. Ass. EURATOM/ENEA/CREATE, Seconda Universita’ di Napoli, Naples, Italy;1. Clinical Microbiology Service, Basurto University Hospital, 18 Avenida Montevideo, 48013, Bilbao, Biscay, Spain;2. Radiodiagnosis Service of Basurto University Hospital, 18 Avenida Montevideo, 48013, Bilbao, Biscay, Spain;3. Biocruces Bizkaia Health Research Institute, Cruces Plaza, 48903, Biscay, Spain;1. Department of Advanced Environmental Science and Engineering, Faculty of Engineering Sciences, Kyushu University, Kasuga-koen 6-1, Kasuga-city, Fukuoka, 816-8580, Japan;2. Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, United Kingdom;3. Thermal Science and Engineering Division, International Institute of Carbon-Neutral Energy Research (I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan |
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| Abstract: | In a recent paper by Chen and Mangasarian (C. Chen, O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problems, Computational Optimization and Applications 2 (1996), 97–138) a class of parametric smoothing functions has been proposed to approximate the plus function present in many optimization and complementarity related problems. This paper uses these smoothing functions to approximate the normal map formulation of nonlinear complementarity problems (NCP). Properties of the smoothing function are investigated based on the density functions that defines the smooth approximations. A continuation method is then proposed to solve the NCPs arising from the approximations. Sufficient conditions are provided to guarantee the boundedness of the solution trajectory. Furthermore, the structure of the subproblems arising in the proposed continuation method is analyzed for different choices of smoothing functions. Computational results of the continuation method are reported. |
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