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Necessary and sufficient second order optimality conditions for multiobjective problems with C1 data
Institution:1. Dpto. de Matemática, Centro Politécnico, Universidade Federal do Paraná,, CEP 81531-980, CP 19081, Curitiba-PR, Brazil;2. Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Facultad de Matemáticas; C/ Tarfia s/; Sevilla, 41012, Spain;4. Grupo de Matemática Aplicada, Dpto. de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Campus Fernando May, Casilla 447, Chillán, Chile;1. Duke University Medical Center, Division of Nephrology, Department of Medicine, Box DUMC 2747, 2424 Erwin Road Suite 605, Durham, NC 27710, USA;2. Durham VA Geriatric Research, Education and Clinical Center, 508 Fulton Street, Durham, NC 27705, USA;3. Duke University Medical Center, Division of Geriatrics, Department of Medicine, Box DUMC 3003, Durham, NC 27710, USA;4. Duke University School of Nursing, DUMC Box 3322, 307 Trent Drive, Durham, NC 27710, USA;5. VA Puget Sound Healthcare System, Department of Medicine and HSR&D Center of Excellence, 1660 S. Columbian Way, Seattle, WA 98108, USA;6. University of Washington, Division of Nephrology, Department of Medicine, 1959 NE Pacific Street, Box 356521, HSB, BB1271, Seattle, WA 98195, USA;1. Department of Mechanical Engineering, Concordia University, Montreal, QC, H3G 1M8 Canada;2. Department of Mechanical Engineering, Concordia University, Montreal, H3G 1M8 Canada;1. Departamento de Geología, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Plaza Ercilla 803, Santiago, Chile;2. Centro de Excelencia en Geotermia de Los Andes (CEGA), Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Plaza Ercilla 803, Santiago, Chile
Abstract:In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency.
Keywords:Multiple objective programming  Generalized convexity  Optimality conditions
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