Constructing Self-concordant Barriers for Convex Cones
نویسندگان
چکیده
منابع مشابه
Constructing self-concordant barriers for convex cones
In this paper we develop a technique for constructing self-concordant barriers for convex cones. We start from a simple proof for a variant of standard result [1] on transformation of a ν-self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter (3.08 √ ν + 3.57)2. Further, we develop a convenient composition theorem for constructing barriers directly fo...
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We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems w...
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In this paper, we give a recursive formula for optimal dual barrier functions on homogeneous cones. This is done in a way similar to the primal construction of Güler and Tunçel [1] by means of the dual Siegel cone construction of Rothaus [2]. We use invariance of the primal barrier function with respect to a transitive subgroup of automorphisms and the properties of the duality mapping, which i...
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We explicitly calculate characteristic functions of cones of generalized polynomials corresponding to Chebyshev systems on intervals of the real line and the circle. Thus, in principle, we calculate homogeneous self-concordant barriers for this class of cones. This class includes almost all "cones of squares" considered in 5]. Our construction, however, does not use this structure and is applic...
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In the study of interior-point methods for nonsymmetric conic optimization and their applications, Nesterov [5] introduced the power cone, together with a 4-selfconcordant barrier for it. In his PhD thesis, Chares [2] found an improved 3-selfconcordant barrier for the power cone. In addition, he introduced the generalized power cone, and conjectured a “nearly optimal” self-concordant barrier fo...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2006
ISSN: 1556-5068
DOI: 10.2139/ssrn.921790