On second-order conditions in vector optimization
Starting from second-order conditions for C 1,1 scalar unconstrained optimization problems described in terms of the second-order Dini directional derivative, we pose the problem, whether similar conditions for C 1,1 vector optimization problems can be derived. We define second-order Dini directional derivatives for vector functions and apply them to formulate such conditions as a Conjecture. The proof of the COnjecture in the case of C1,1 function (called the nonsmooth case) will be given in another paper. The present paper provides the background leading to its correct formulation. Using Lagrange multipliers technique, we prove the COnjecture in the case of twice Fréchet differentiable function (called the smooth case) and show on example the effectiveness of the obtained conditions. Another example shows, that in the nonsmooth case it is important to take into account the whole set of Lagrange multipliers, instead of dealing with a particular multiplier.
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- Antoine Magnier & Joël Toujas-Bernate, 1994. "Technology and trade: Empirical evidences for the major five industrialized countries," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 130(3), pages 494-520, September.
- Keith E. Maskus, 1991. "Comparing International Trade Data and Product and National Characteristics Data for the Analysis of Trade Models," NBER Chapters, in: International Economic Transactions: Issues in Measurement and Empirical Research, pages 17-60 National Bureau of Economic Research, Inc.
- Gene M. Grossman & Elhanan Helpman, 1994.
"Technology and Trade,"
NBER Working Papers
4926, National Bureau of Economic Research, Inc.
- Giovanni Amendola & Giovanni Dosi & Erasmo Papagni, 1993. "The dynamics of international competitiveness," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 129(3), pages 451-471, September.
- Laursen, Keld, 1999.
"The impact of technological opportunity on the dynamics of trade performance,"
Structural Change and Economic Dynamics,
Elsevier, vol. 10(3-4), pages 341-357, December.
- Keld Laursen, 1996. "The Impact of Technological Opportunity on the Dynamics of Trade Performance," DRUID Working Papers 96-12, DRUID, Copenhagen Business School, Department of Industrial Economics and Strategy/Aalborg University, Department of Business Studies.
- L.R. de Mello Jr., 1996.
"Foreign Direct Investment-Led Growth: Evidence from Time Series and Panel Data,"
Studies in Economics
9615, School of Economics, University of Kent.
- de Mello, Luiz R, Jr, 1999. "Foreign Direct Investment-Led Growth: Evidence from Time Series and Panel Data," Oxford Economic Papers, Oxford University Press, vol. 51(1), pages 133-51, January.
- Bell, Martin & Albu, Michael, 1999. "Knowledge Systems and Technological Dynamism in Industrial Clusters in Developing Countries," World Development, Elsevier, vol. 27(9), pages 1715-1734, September.
- Franco Malerba & Fabio Montobbio, 2000. "Knowledge Flows, Structure of Innovative Activity and International Specialization," KITeS Working Papers 119, KITeS, Centre for Knowledge, Internationalization and Technology Studies, Universita' Bocconi, Milano, Italy, revised Nov 2000.
- Jan Fagerberg & Gunnar Sollie, 1987. "The method of constant market shares analysis reconsidered," Working Papers Archives 1987001, Centre for Technology, Innovation and Culture, University of Oslo.
- Bas ter Weel & L. Soete & B. Verspagen, 2010.
"Systems of innovation,"
CPB Discussion Paper
138, CPB Netherlands Bureau for Economic Policy Analysis.
- Krugman, Paul, 1979. "A Model of Innovation, Technology Transfer, and the World Distribution of Income," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 253-66, April.
- Chui, Michael, et al, 2002. " North-South Models of Growth and Trade," Journal of Economic Surveys, Wiley Blackwell, vol. 16(2), pages 123-65, April.
- Greenhalgh, Christine, 1990. "Innovation and Trade Performance in the United Kingdom," Economic Journal, Royal Economic Society, vol. 100(400), pages 105-18, Supplemen.
- Jan Fagerberg, 1988.
Working Papers Archives
1988001, Centre for Technology, Innovation and Culture, University of Oslo.
- Fabio Montobbio, 2003. "Sectoral patterns of technological activity and export market share dynamics," Cambridge Journal of Economics, Oxford University Press, vol. 27(4), pages 523-545, July.
- Lall, Sanjaya & Teubal, Morris, 1998. ""Market-stimulating" technology policies in developing countries: A framework with examples from East Asia," World Development, Elsevier, vol. 26(8), pages 1369-1385, August.
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