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A Computational Study of the Homogeneous Algorithm for LargeScale Convex Optimization
, 1997
"... Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of th ..."
Abstract

Cited by 13 (1 self)
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Recently the authors have proposed a homogeneous and selfdual algorithm for solving the monotone complementarity problem (MCP) [5]. The algorithm is a single phase interiorpoint type method, nevertheless it yields either an approximate optimal solution or detects a possible infeasibility of the problem. In this paper we specialize the algorithm to the solution of general smooth convex optimization problems that also possess nonlinear inequality constraints and free variables. We discuss an implementation of the algorithm for largescale sparse convex optimization. Moreover, we present computational results for solving quadratically constrained quadratic programming and geometric programming problems, where some of the problems contain more than 100,000 constraints and variables. The results indicate that the proposed algorithm is also practically efficient. Department of Management, Odense University, Campusvej 55, DK5230 Odense M, Denmark. Email: eda@busieco.ou.dk y ...
A unified kernel function approach to polynomial interiorpoint algorithms for the Cartesian P∗(κ)SCLCP ∗
, 2010
"... Recently, Bai et al. [Bai Y.Q., Ghami M. El, Roos C., 2004. A comparative study of kernel functions for primaldual interiorpoint algorithms in linear optimization. SIAM Journal on Optimization, 15(1), 101128.] provided a unified approach and comprehensive treatment of interiorpoint methods for l ..."
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Recently, Bai et al. [Bai Y.Q., Ghami M. El, Roos C., 2004. A comparative study of kernel functions for primaldual interiorpoint algorithms in linear optimization. SIAM Journal on Optimization, 15(1), 101128.] provided a unified approach and comprehensive treatment of interiorpoint methods for linear optimization based on the class of eligible kernel functions. In this paper we generalize the analysis presented in the above paper to the Cartesian P∗(κ)linear complementarity problem over symmetric cones via the machinery of the Euclidean Jordan algebras. The symmetry of the resulting search directions is forced by using the NesterovTodd scaling scheme. The iteration bounds for the algorithms are performed in a systematic scheme, which highly depend on the choice of the eligible kernel functions. Moreover, we derive the iteration bounds that match the currently best known iteration bounds for large and smallupdate methods, namely O((1 + 2κ) √ r log r log r ε) and O((1 + 2κ) √ r log r), respectively, where r denotes the rank of the associated Euclidean Jordan ε algebra and ε the desired accuracy.