A practicable way for computing the directional derivative of the optimal value function in convex programming

References

• Barthelemy , J.F.M. and Sobieszczanski-Sobieski , J. 1983 . Optimum sensitivity derivatives of objective functions in nonlinear programming . AIAA J , 21 ( 6 ) : 913 – 915 .
   Google Scholar
• Baumgart , R. 1992 . The set of coefficients such that zero is contained in the weighted algebraic sum of polyhedral sets . Wiss. Z. Tech. Univ. Chemnitz , 34 ( 1 ) : 21 – 30 .
   Google Scholar
• Beer , K. 1984 . Verfahren der zulässigen Richtungen für nichtlineare konvexe Optimierungsprobleme mit Verbundstruktur . Wiss. Berichte Tech. Hochsch. Leipzig , 2 ( 1 ) : 35 – 47 .
   Google Scholar
• Beer , K. and Brand , M. 1986 . Zur Berechnung von Richtungen, in denen die Ableitung der Optimalwertfunktion einer LOA extremale Werte hat . Wiss. Z. Tech. Hochsch. Karl-Marx-Stadt , 28 ( 2 ) : 181 – 187 .
   Google Scholar
• Dem'yanov , V.F. and Malozemov , A.M. 1974 . Introduction to Minimax , New York : John Wiley & Sons . (Transl. from the Russian)
   Google Scholar
• Dem'yanov , V.F. and Vasil'ev , L.V. 1986 . Nondifferentiable Optimization , New York : Optimization Software . (Transl. from the Russian)
   Google Scholar
• Fiacco , A.V. 1983 . Introduction to Sensitivity and Stability Analysis in Nonlinear Programming , New York : Academic Press .
   Google Scholar
• Fedorov , V.V. 1979 . Numerical Max-Min Methods , Moscow : Nauka . (in Russian)
   Google Scholar
• Gantmakher , F.R. 1970 . “ Matrizenrechnung ” . In Teil 1 , Berlin : Deutscher Verlag der Wissenschaften . (Transl. from the Russian)
   Google Scholar
• Gauvin , J. and Dubeau , F. 1982 . Differential properties of the marginal function in mathematical programming . Math. Programming Stud , 19 : 101 – 119 .
   Web of Science ®Google Scholar
• Gol'stein , E.G. 1973 . “ Konvexe Optimierung ” . In Elemente der Theorie , Vol. WTB 122 , Berlin : Akademie-Verlag . (Trans. from the Russian)
   Google Scholar
• Janin , R. 1984 . Directional derivative of the marginal function in nonlinear programming . Math.Programming Stud , 21 : 110 – 126 .
   Web of Science ®Google Scholar
• Kiwiel , K.G. 1985 . Methods of Descent for Nondifferentiable Optimization , New York : Springer .
   Google Scholar
• Lemaréchal , C. 1980 . “ Nondifferentiable optimization ” . In Nonlinear Optimization, Theory and Algorithms , Edited by: Dixon , L.C.W. , Spedicato , E. and Szegö , G. Boston : Birkhäuser .
   Google Scholar
• Luderer , B. 1991 . Directional derivative estimates for the otpimal value function of aquasidifferentiable programming problem . Math. Programming , 51 ( 3 ) : 333 – 348 .
   Web of Science ®Google Scholar
• Nožička , F. , Grygarová , L. and Lommatzsch , K. 1988 . Geometrie konvexer Mengen und konvexe Analysis , Berlin : Akademie-Verlag .
   Google Scholar
• Owen , G. 1968 . Game Theory , Philadelphia : Saunders Company .
   Google Scholar
• Polyak , B.T. 1987 . Introduction to Optimization , New York : Optimization Software . (Transl. from the Russian)
   Google Scholar
• Rockafellar , R.T. 1970 . Convex Analysis , Princeton : Princeton University Press .
   Google Scholar
• Rockafellar , R.T. 1984 . Directional differentiability of the optimal value function in a nonlinear programming problem . Math. Programming Stud , 21 : 213 – 226 .
   Web of Science ®Google Scholar
• Schwartz , B. and Käschel , J. 1981 . Verfahren der zulässigen Richtungen für Optimierungsaufgaben mit nichtdifferenzierbaren Funktionen und Dekomposition . Wiss. Schriftenreihe Tech. Hochsch.Karl-Marx-Stadt , 11
   Google Scholar
• Shor , N.Z. 1985 . Minimization Methods for Non-Differentiable Functions , Berlin : Springer . (Transl.from the Russian)
   Google Scholar
• Sukharev , A.G. 1989 . Minimax Algorithms in Problems of Numerical Analysis , Moscow : Nauka . (in Russian)
   Google Scholar
• Williams , A.C. 1963 . Marginal values in linear programming . J. Soc. Indust. Appl. Math , 11 ( 1 ) : 82 – 94 .
   Google Scholar
• Würker U. The method of feasible directions for minimax problems Optimization 1993 appear
   Google Scholar