Graph implementations for nonsmooth convex programs

被引：2126

作者：

Stanford University, United States ^{[1
]}

机构：

来源：

Lect. Notes Control Inf. Sci. | 2008年 / 95-110期

关键词：

Conic optimization; Convex optimization; Disciplined convex programming; Nondifferentiable functions; Nonsmooth optimization; Optimization modeling languages; Second-order cone programming; Semidefinite programming;

D O I：

10.1007/978-1-84800-155-8_7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We describe graph implementations, a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework. This simple and natural idea allows a very wide variety of smooth and nonsmooth convex programs to be easily specified and efficiently solved, using interior-point methods for smooth or cone convex programs. © 2008 Springer London.

引用

页码：95 / 110

页数：15

共 17 条

[1]

Alizadeh F., Goldfarb D., Second-order cone programming (January, (2004)

[2]

Bertsekas D.P., Convex Analysis and Optimization, (2003)

[3]

Bland R., Goldfarb D., Todd M., The ellipsoid method: A survey, Operations Research, 29, 6, pp. 1039-1091, (1981)

[4]

Borwein J., Lewis A., Convex Analysis and Nonlinear Optimization: Theory and Examples, (2000)

[5]

Ben-Tal A., Nemirovski A., Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications, MPS/SIAM Series on Optimization, (2001)

[6]

Boyd S., Vandenberghe L., Convex Optimization, (2004)

[7]

Dantzig G., Linear Programming and Extensions, (1963)

[8]

Grant M., (2004)

[9]

Lofberg J., YALMIP: A toolbox for modeling and optimization in MATLAB®, Proceedings of the CACSD Conference, (2004)

[10]

Lobo M., Vandenberghe L., Boyd S., Lebret H., Applications of second-order cone programming. Linear Algebra and its Applications, 284, pp. 193-228, (1998)

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