, Interior path-following primal-dual algorithms. part II: Convex quadratic programming, Mathematical Programming, 44 (1989), pp. 43--66.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....was partly supported by the Office of Naval Research under grants N00014 93 1 0234 and N00014 941 0340. Their financial support is gratefully acknowledged. y School of Industrial and Systems Engineering, Georgia Tech, Atlanta, GA 30332. monteiro isye.gatech.edu) 1 [9] and Monteiro and Adler [12, 13], referred in here to as the short step path following method, improves the worst case iteration complexity of the algorithm of [10] by a factor of p n by generating iterates in a narrower neighborhood of the central path. Several authors have discussed generalizations of interior point ....

....Kojima, Shindoh and Hara [11] and Nesterov and Todd [18] present some algorithms which extend the primal dual methods for linear programming based on the scaling X 1=2 S Gamma1=2 . In particular, they both provide short step path following methods for SDP which generalize the algorithm in [9, 12, 13]; however, no extensions of the long step path following algorithm in [10] are provided. In fact, Kojima, Shindoh and Hara mention in section 9 of [11] that they encountered difficulty in providing such an extension. In this paper, by characterizing two of the search directions introduced in [11] ....

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, Interior path-following primal-dual algorithms. part II: Convex quadratic programming, Mathematical Programming, 44 (1989), pp. 43--66.

....methods. The first algorithms for SDP which are extensions of well known primal dual LP algorithms, such as the long step path following algorithm of Kojima, Mizuno and Yoshise [7] and Tanabe [31, 32] the short step path following algorithm of Kojima, Mizuno and Yoshise [6] and Monteiro and Adler [17, 18], and the predictor corrector algorithm of Mizuno, Todd and Ye [14] use one of the following three search directions: i) the Alizadeh, Haeberly and Overton (AHO) direction proposed in [2] ii) a direction independently proposed by Helmberg, Rendl, Vanderbei and Wolkowicz [4] and Kojima, Shindoh ....

, Interior path-following primal-dual algorithms. Part II: Convex quadratic programming, Mathematical Programming, 44 (1989), pp. 43--66.

....are concentrated on primal dual methods. The first SDP algorithms that are extensions of primal dual LP algorithms, such as the longstep path following algorithm of Kojima, Mizuno and Yoshise [9] the short step path following algorithm of Kojima, Mizuno and Yoshise [8] and Monteiro and Adler [18, 19], and the predictorcorrector algorithm of Mizuno, Todd and Ye [16] use one of the following three search directions: i) the Alizadeh, Haeberly and Overton (AHO) direction proposed in [2] ii) a direction independently proposed by Kojima, Shindoh and Hara [13] and Helmberg, Rendl, Vanderbei and ....

.... our techniques by showing the polynomiality of two primal dual feasible algorithms based on the MZ unified direction: a short step path following method and a predictorcorrector method which are extensions of the LP algorithms studied in Kojima, Mizuno and Yoshise [8] Monteiro and Adler [18, 19], and Mizuno, Todd and Ye [16] The iteration complexity bounds for both algorithms are shown to be exactly the same as their corresponding LP algorithms, namely O( p nL) iterations to reduce the duality gap by a factor of at least 2 GammaO(L) As opposed to Monteiro and Zhang [21] which ....

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, Interior path-following primal-dual algorithms. Part II: Convex quadratic programming, Mathematical Programming, 44 (1989), pp. 43--66.

....semidefinite analog of convex quadratic programming or, more generally, a semidefinite analog of the linear complementarity problem. Also, one can study a semidefinite analog of linear fractional programs. For the linear version of all these problems interior point methods have been published (see [45], 37] and [4] for example) and one can apply the conversion rules mentioned above to obtain interior point methods for their semidefinite variants. Details are omitted here. 3.5. Differences between SDP and LP interior point algorithms. Thus far, we have emphasized the similarity of linear and ....

, Interior path following primal--dual algorithms. Part II: Convex quadratic programming, Math. Programming, 44 (1989), pp. 43--66.

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