Abstract
This paper extends and analyzes a new potentla1 reduction algorithm for solving smooth convex programming. Under a kind of strict feasibility assumption. we show that the algorithm under modification requires a total of number of iterations, and the total arithmetic operations are not more than , where and l is the initial input size. As an application to usual linear or convex quadratic programming. this algorithm solves the pair of primal and dual PI-oblems in at most iterations. and the total arithmetic operations are shown to be of the order of where L is the input size
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