Enhanced Basic Procedures for the Projection and Rescaling Algorithm

Gutman, David H.

doi:10.48550/arxiv.1807.05982

Cited by 1 publication

(2 citation statements)

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“…The algorithm described here has its origins in a previous work by Chubanov [4], which proposed a polynomial algorithm to compute an interior feasible solution of homogeneous linear programming problems. Chubanov's original algorithm was extended and improved along several different directions [16,23,20,15,18,8,21,24,12]. Nevertheless, a common point among most of those variants is that they are divided in two parts, a basic procedure and a main algorithm.…”

Section: Previous Work On Projection and Rescaling Algorithmsmentioning

confidence: 99%

“…Roos [23] proposed an improved basic procedure which generates sharper cuts and also produced some preliminary numerical results. Improved basic procedures were also proposed by Zhang and Roos [24] and by Gutman [12]. Li, Roos and Terlaky [16] extended Chubanov's algorithm to the case of linear feasibility problems with a single non-homogeneous equality.…”

Section: Previous Work On Projection and Rescaling Algorithmsmentioning

confidence: 99%

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An oracle-based projection and rescaling algorithm for linear semi-infinite feasibility problems and its application to SDP and SOCP

Muramatsu,

Kitahara,

Lourenço

et al. 2018

Preprint

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We point out that Chubanov's oracle-based algorithm for linear programming [5] can be applied almost as it is to linear semi-infinite programming (LSIP). In this note, we describe the details and prove the polynomial complexity of the algorithm based on the real computation model proposed by Blum, Shub and Smale (the BSS model) which is more suitable for floating point computation in modern computers. The adoption of the BBS model makes our description and analysis much simpler than the original one by Chubanov [5]. Then we reformulate semidefinite programming (SDP) and second-order cone programming (SOCP) into LSIP, and apply our algorithm to obtain new complexity results for computing interior feasible solutions of homogeneous SDP and SOCP.

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