Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones
نویسندگان
چکیده
We describe an implementation of nonsymmetric interior-point methods for linear cone programs defined by two types of matrix cones: the cone of positive semidefinite matrices with a given chordal sparsity pattern and its dual cone, the cone of chordal sparse matrices that have a positive semidefinite completion. The implementation takes advantage of fast recursive algorithms for evaluating the function values and derivatives of the logarithmic barrier functions for these cones. We present experimental results of two implementations, one of which is based on an augmented system approach, and a comparison with publicly available interior-point solvers for semidefinite programming. Mathematics Subject Classification (2000) 90-08 Mathematical Programming computational methods · 90C06 Mathematical Programming large-scale · 90C22 Mathematical Programming semidefinite programing · 90C25 Mathematical Programming convex programming · 90C51 Mathematical Programming interior-point methods The authors’ (Andersen and Vandenberghe) research was supported in part by NSF grants ECS-0524663 and ECCS-0824003. M. S. Andersen (B) · L. Vandenberghe Electrical Engineering Department, University of California, Los Angeles, USA e-mail: [email protected] L. Vandenberghe e-mail: [email protected] J. Dahl MOSEK ApS, Fruebjergvej 3, 2100 Copenhagen Ø, Denmark e-mail: [email protected]
منابع مشابه
A full NT-step O(n) infeasible interior-point method for Cartesian P_*(k) –HLCP over symmetric cones using exponential convexity
In this paper, by using the exponential convexity property of a barrier function, we propose an infeasible interior-point method for Cartesian P_*(k) horizontal linear complementarity problem over symmetric cones. The method uses Nesterov and Todd full steps, and we prove that the proposed algorithm is well define. The iteration bound coincides with the currently best iteration bound for the Ca...
متن کاملLogarithmic barriers for sparse matrix cones
Algorithms are presented for evaluating gradients and Hessians of logarithmic barrier functions for two types of convex cones: the cone of positive semidefinite matrices with a given sparsity pattern, and its dual cone, the cone of sparse matrices with the same pattern that have a positive semidefinite completion. Efficient large-scale algorithms for evaluating these barriers and their derivati...
متن کامل1 Interior - point methods for large - scale cone programming
In the conic formulation of a convex optimization problem the constraints are expressed as linear inequalities with respect to a possibly non-polyhedral convex cone. This makes it possible to formulate elegant extensions of interior-point methods for linear programming to general nonlinear convex optimization. Recent research on cone programming algorithms has particularly focused on three conv...
متن کاملOn implementing a primal-dual interior-point method for conic quadratic optimization
Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can ...
متن کاملAn improved infeasible interior-point method for symmetric cone linear complementarity problem
We present an improved version of a full Nesterov-Todd step infeasible interior-point method for linear complementarityproblem over symmetric cone (Bull. Iranian Math. Soc., 40(3), 541-564, (2014)). In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three - centering steps. Here, each iteration consists of only a feasibility step. Thus, the new...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Program. Comput.
دوره 2 شماره
صفحات -
تاریخ انتشار 2010