This section deals mainly with the problem of minimization of the function f : D → R over the closed convex subset K ⊂ D. The domain D ⊂ R n , in general, may not coincide with the whole space R n . However, in order to avoid considering the boundary effects, we will always assume that D is and open set. Thus, the closed subset K is contained in the interior of D. It is traditional to consider two classes of these problems: the case of continuously diffjerentiable function f and the case of convex function f.
KeywordsLagrange Multiplier Variational Inequality Optimization Model Convex Function Linear Form
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- Arrow, K.J., Hurwicz, L., Uzawa, H. Studies in Linear and Nonlinear Programming. Stanford: Stanford University Press, 1958.Google Scholar
- Bulavsky, VA. 1.‘Feedback in Optimization Problems’. In: Proceedings of Institute of Mathematics of the USSR Academy of Sciences, Novosibirsk, 1988; 10: 55–63 (in Russian).Google Scholar
- Bulavsky, VA. 2. ‘Local Estimates and the Selection Problem’. In: Modern Mathematical Methods of Optimization, K.-H. Elster, ed., Berlin: Academic-Verlag, 1993.Google Scholar
- Bulavsky, VA. 3. Quasilinear programming and vector optimization. Soviet Math. Dokl. 1981; 23(2): 328–332.Google Scholar
- Clarke, F.H. Optimization and Non-Smooth Analysis. New York: Wiley Interscience, 1983.Google Scholar
- Convex Cones, Sets, and Functions. Notes of Lectures at Princeton University, 1951.Google Scholar
- Keeney, R.L., Raiffa, H. Decisions with Multiple Objectives: Preferences and Value Tradeoffs. New York: Wiley, 1976.Google Scholar
- Kuhn, HW, Tucker, AW. ‘Nonlinear Programming’. In: Proceedings of the Secofid Berkeley Symposium on Mathematics, Statistics and Probability. Berkeley: University of California Press, 1951.Google Scholar
- Samuelson, P.A. Foundations of Economic Analysis. Harvard: Harvard University press, 1948.Google Scholar