دوگانگی (بهینه‌سازی)
نوشته‌ها

↑  Boyd, Stephen P.; Vandenberghe, Lieven (2004). Convex Optimization (pdf). Cambridge University Press. ISBN 978-0-521-83378-3. Retrieved October 15, 2011.
1 2  Boţ, Radu Ioan; Wanka, Gert; Grad, Sorin-Mihai (2009). Duality in Vector Optimization. Springer. ISBN 978-3-642-02885-4.
↑  Csetnek, Ernö Robert (2010). Overcoming the failure of the classical generalized interior-point regularity conditions in convex optimization. Applications of the duality theory to enlargements of maximal monotone operators. Logos Verlag Berlin GmbH. ISBN 978-3-8325-2503-3.
↑  Zălinescu, Constantin (2002). Convex analysis in general vector spaces. River Edge, NJ: World Scientific Publishing Co. , Inc. pp. 106–113. ISBN 981-238-067-1. MR 1921556.
↑  Borwein, Jonathan; Zhu, Qiji (2005). Techniques of Variational Analysis. Springer. ISBN 978-1-4419-2026-3.
↑  Ahuja, Ravindra K.; Magnanti, Thomas L.; and Orlin, James B. (1993). Network Flows: Theory, Algorithms and Applications. Prentice Hall. ISBN 0-13-617549-X.{{cite book}}:  نگهداری یادکرد:نام‌های متعدد:فهرست نویسندگان (link)
↑  Bertsekas, Dimitri P. (1999). Nonlinear Programming (2nd ed.). Athena Scientific. ISBN 1-886529-00-0.
↑  Bonnans, J.  Frédéric; Gilbert, J.  Charles; Lemaréchal, Claude; Sagastizábal, Claudia A. (2006). Numerical optimization: Theoretical and practical aspects. Universitext (Second revised ed. of translation of 1997 French ed.). Berlin: Springer-Verlag. pp. xiv+490. doi:10.1007/978-3-540-35447-5. ISBN 3-540-35445-X. MR 2265882.
↑  Hiriart-Urruty, Jean-Baptiste; Lemaréchal, Claude (1993). Convex analysis and minimization algorithms, Volume I: Fundamentals. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Vol. 305. Berlin: Springer-Verlag. pp. xviii+417. ISBN 3-540-56850-6. MR 1261420.
↑  Hiriart-Urruty, Jean-Baptiste; Lemaréchal, Claude (1993). "14 Duality for Practitioners". Convex analysis and minimization algorithms, Volume II: Advanced theory and bundle methods. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Vol. 306. Berlin: Springer-Verlag. pp. xviii+346. ISBN 3-540-56852-2. MR 1295240.{{cite book}}:  نگهداری CS1: نقطه‌گذاری اضافه (link)
↑  Lasdon, Leon S. (2002) [Reprint of the 1970 Macmillan]. Optimization theory for large systems. Mineola, New York: Dover Publications, Inc. pp. xiii+523. ISBN 978-0-486-41999-2. MR 1888251.
↑  Lemaréchal, Claude (2001). "Lagrangian relaxation".  In Jünger, Michael; and Naddef, Denis (ed.). Computational combinatorial optimization: Papers from the Spring School held in Schloß Dagstuhl, May 15–19, 2000. Lecture Notes in Computer Science (LNCS). Vol. 2241. Berlin: Springer-Verlag. pp. 112–156. doi:10.1007/3-540-45586-8_4. ISBN 3-540-42877-1. MR 1900016.{{cite book}}:  نگهداری یادکرد:نام‌های متعدد:فهرست ویراستاران (link)
↑  Minoux, Michel (1986). Mathematical programming: Theory and algorithms (Translated by Steven Vajda from the (1983 Paris: Dunod) French ed.). Chichester: A Wiley-Interscience Publication. John Wiley & Sons, Ltd. pp. xxviii+489. ISBN 0-471-90170-9. MR 0868279. (2008 Second ed. , in French: Programmation mathématique: Théorie et algorithmes, Éditions Tec & Doc, Paris, 2008. xxx+711 pp.). {{cite book}}: Unknown parameter |note= ignored (help)
↑  Shapiro, Jeremy F. (1979). Mathematical programming: Structures and algorithms. New York: Wiley-Interscience [John Wiley & Sons]. pp. xvi+388. ISBN 0-471-77886-9. MR 0544669.
↑  Geoffrion, Arthur M. (1971). "Duality in Nonlinear Programming: A Simplified Applications-Oriented Development". SIAM Review. 13 (1): 1–37. doi:10.1137/1013001. JSTOR 2028848.
↑  jemdoc. "Dual Problem" (به انگلیسی). Archived from the original on 27 December 2014. Retrieved 29 January 2017.
↑  Boyd، stephan (۲۰۰۴). convex optimization. newyork: Cambridge university press.