Abstract
We present a primal-dual path following interior algorithm for a class of linearly constrained convex programming problems with non-negative decision variables. We introduce the definition of a Scaled Lipschitz Condition and show that if the objective function satisfies the Scaled Lipschitz Condition then, at each iteration, our algorithm reduces the duality gap by at least a factor of (1−δ/√n), whereδ is positive and depends on the curvature of the objective function, by means of solving a system of linear equations which requires no more than O(n3) arithmetic operations. The class of functions having the Scaled Lipschitz Condition includes linear, convex quadratic and entropy functions.
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Zhu, J. A path following algorithm for a class of convex programming problems. ZOR Zeitschrift für Operations Research Methods and Models of Operations Research 36, 359–377 (1992). https://doi.org/10.1007/BF01416235
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DOI: https://doi.org/10.1007/BF01416235