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    STUDIA INFORMATICA - Issue no. 2 / 2009  

  Abstract:  In a recent paper we have introduced a new class of search directions for solving linear optimization (LO) problems. These directions are based on an algebraic equivalent transformation of the nonlinear equation from the system which defines the central path. However, from the implementation point of view predictor-corrector algorithms proved to be the most efficient among the class of interior point methods (IPMs). Therefore, we have defined also other variants of this class of algorithms, for example a weighted path-following algorithm, and a predictor-corrector algorithm for LO problems. Recently, the technique of finding search directions has been applied with success for linearly constrained convex optimization (LCCO), by Zhang, Bai and Wang. In this paper we define a new predictor-corrector algorithm for solving LCCO problems. We obtain new search directions by applying the method of algebraic equivalent transformation in this case too. Polynomial complexity of this algorithm is proved.

Key words and phrases. Linearly constrained convex optimization, interior-point methods, predictor-corrector algorithm, equivalent algebraic transformation, centering equation, Newton step.
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