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On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming. (English) Zbl 0913.65050
The author considers primal-dual interior-point algorithms for solving semidefinite programs of the form \[ C\cdot X\to \min,\quad A_i\cdot X= b_i,\quad i=1,\dots, m,\quad X\geq 0, \] where \(C\), \(X\) and \(A_i\) are symmetric matrices in \(\mathbb{R}^{n\times n}\), \(b_i\in\mathbb{R}\) and \(C\cdot X= \text{tr}(CX)\).
A concise derivation of the key equalities and inequalities for complexity analysis along the exact line used linear programming are given and basic relationships that have compact forms almost identical to their counterparts in linear programming are produced. Examples are presented.

65K05 Numerical mathematical programming methods
90C05 Linear programming
65Y20 Complexity and performance of numerical algorithms
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