Convex optimization in Julia
作者： Madeleine Udell , Karanveer Mohan , David Zeng , Jenny Hong , Steven Diamond
关键词: Proper convex function 、 Mathematics 、 Subderivative 、 Convex optimization 、 Linear matrix inequality 、 Mathematical optimization 、 Convex analysis 、 Conic optimization 、 Convex hull 、 Algorithm 、 Absolutely convex set
摘要: This paper describes Convex1, a convex optimization modeling framework in Julia. Convex translates problems from user-friendly functional language into an abstract syntax tree describing the problem. concise representation of global structure problem allows to infer whether complies with rules disciplined programming (DCP), and pass suitable solver. These operations are carried out Julia us- ing multiple dispatch, which dramatically reduces time required verify DCP compliance parse conic form. then automatically chooses appropriate backend solver solve form
acm.org
computer.org
stanford.edu
arxiv-vanity.com参考文章(38)
Lubomir V. Kolev, Daniel H. Fylstra, Ivo P. Nenov, Convexity Determination in the Microsoft Excel Solver Using Automatic Differentiation Techniques ,(2004)
Michael R. Bussieck, Alex Meeraus, General Algebraic Modeling System (GAMS) Springer, Boston, MA. pp. 137- 157 ,(2004) , 10.1007/978-1-4613-0215-5_8
Romesh Saigal, Lieven Vandenberghe, Henry Wolkowicz, Handbook of semidefinite programming : theory, algorithms, and applications Kluwer Academic Publishers. ,(2000)
Stephen Boyd, Madeleine Udell, Bounding Duality Gap for Problems with Separable Objective arXiv: Optimization and Control. ,(2014)
Eric Chu, Neal Parikh, Alexander Domahidi, Stephen Boyd, Code generation for embedded second-order cone programming european control conference. pp. 1547- 1552 ,(2013) , 10.23919/ECC.2013.6669712
Yurii Nesterov, Arkadii Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming ,(1987)
Laurence A. Wolsey, George L. Nemhauser, Integer and Combinatorial Optimization ,(1988)
Boris Houska, Hans Joachim Ferreau, Moritz Diehl, ACADO toolkit-An open-source framework for automatic control and dynamic optimization Optimal Control Applications and Methods. ,vol. 32, pp. 298- 312 ,(2011) , 10.1002/OCA.939
Jeff Bezanson, Viral Shah, Jiahao Chen, Alan Edelman, Stefan Karpinski, Array Operators Using Multiple Dispatch: A design methodology for array implementations in dynamic languages Proceedings of ACM SIGPLAN International Workshop on Libraries, Languages, and Compilers for Array Programming. pp. 56- 61 ,(2014) , 10.1145/2627373.2627383
L.T. Biegler, V.M. Zavala, Large-scale nonlinear programming using IPOPT: An integrating framework for enterprise-wide dynamic optimization Computers & Chemical Engineering. ,vol. 33, pp. 575- 582 ,(2009) , 10.1016/J.COMPCHEMENG.2008.08.006