Notes on Parametric Quadratic Programming
نویسنده
چکیده
The primal-dual algorithm of parametric linear programming (e.g. {l]) can be extended in some sence to parametric quadratic programming problems as follows. § 1. Problem of the first type Let us consider the following quadratic programming problem PIA with a parameter A. where C is an n X n positive semi-definite matrix, A is an m X n matrix, p and x are n-vectors, and band d are m-vectors. We denote by M' the transpose of M. Dorn[ 2] constructed the dual problem DIA of PIA with a vector variable y: DIA: Max{p'x+x'Cx+y'(Ax-b-,{d)IP+2Cx+A' The duality theorem holds between PIA and DIA as in linear programming. Now let (x, y) be the optimal solution of PI). and DIL The restricted primal and dual problems which we denote by RP and RD are constructed as follows.
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