B. Kalantari, Karmarkar's algorithm with improved steps, Math. Programming, 46 (1990), pp. 73-78. Home/Search Document Not in Database Summary Related Articles Check |
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Scaling Dualities And Self-Concordant Homogeneous Programming In .. - Kalantari (1998) Self-citation (Kalantari) (Correct)
....2.2 Scaling dualities Scaling dualities are theorems of the alternative that relate exact and # approximate solvability of the four problems HP, SP, HSP, and ASP. We shall summarize these scaling dualities over the nonnegative orthant. These dualities have been established in the papers Kalantari [12], 13] 14] and [17] SCALING DUALITIES AND HOMOGENEOUS PROGRAMMING 8 The connection between linear programming and matrix scaling was established in Kalantari [13] via a scaling duality. In a subsequent technical report, Kalantari [14] whose more general version appeared as Kalantari [17] ....
....d # stated above. In view of the scaling dualities the algorithm is also capable of solving a decision version of SP, HSP, or ASP. For a description of this algorithm, as applied to Karmarkar s canonical LP, and its general case of arbitrary convex HP over the nonnegative orthant, see Kalantari [12] and [15] respectively. 2.3.2 A potential reduction algorithm The projective algorithm, stated above, tests the solvability of HP, but only a decision version of the remaining three problems, SP, HSP, or ASP. This projective algorithm can be viewed as a homogeneous potential reduction algorithm. ....
B. Kalantari, Karmarkar's algorithm with improved steps, Math. Programming, 46 (1990), pp. 73-78.
Scaling Dualities And Self-Concordant Homogeneous Programming In .. - Kalantari (1998) Self-citation (Kalantari) (Correct)
....Scaling dualities. Scaling dualities are theorems of the alternative that relate exact and ffl approximate solvability of the four problems HP, SP, HSP, and ASP. We shall summarize these scaling dualities over the nonnegative orthant. These dualities have been established in the papers Kalantari [12], 13] 14] and [17] The connection between linear programming and matrix scaling was established in Kalantari [13] via a scaling duality. In a subsequent technical report, Kalantari [14] whose more general version appeared as Kalantari [17] it was proved that the stationary points of and ....
....d 0 stated above. In view of the scaling dualities the algorithm is also capable of solving a decision version of SP, HSP, or ASP. For a description of this algorithm, as applied to Karmarkar s canonical LP, and its general case of arbitrary convex HP over the nonnegative orthant, see Kalantari [12] and [15] respectively. 2.3.2. A potential reduction algorithm. The projective algorithm, stated above, tests the solvability of HP, but only a decision version of the remaining three problems, SP, HSP, or ASP. This projective algorithm can be viewed as a homogeneous potential reduction ....
B. Kalantari, Karmarkar's algorithm with improved steps, Math. Programming, 46 (1990), pp. 73-78.
Scaling Dualities And Self-Concordant Homogeneous.. - Bahman Kalantari (1998) Self-citation (Kalantari) (Correct)
....Scaling dualities. Scaling dualities are theorems of the alternative that relate exact and # approximate solvability of the four problems HP, SP, HSP, and ASP. We shall summarize these scaling dualities over the nonnegative orthant. These dualities have been established in the papers Kalantari [12], 13] 14] and [17] The connection between linear programming and matrix scaling was established in Kalantari [13] via a scaling duality. In a subsequent technical report, Kalantari [14] whose more general version appeared as Kalantari [17] it was proved that the stationary points of and X ....
....d # stated above. In view of the scaling dualities the algorithm is also capable of solving a decision version of SP, HSP, or ASP. For a description of this algorithm, as applied to Karmarkar s canonical LP, and its general case of arbitrary convex HP over the nonnegative orthant, see Kalantari [12] and [15] respectively. 2.3.2. A potential reduction algorithm. The projective algorithm, stated above, tests the solvability of HP, but only a decision version of the remaining three problems, SP, HSP, or ASP. This projective algorithm can be viewed as a homogeneous potential reduction ....
B. Kalantari, Karmarkar's algorithm with improved steps, Math. Programming, 46 (1990), pp. 73-78.
On The Arithmetic-Geometric Mean Inequality And Its.. - Bahman Kalantari Self-citation (Kalantari) (Correct)
....by Theorem 2. 1 can be stated in much more generality, where the underlying cone is an arbitrary closed convex pointed cone, and OE an arbitrary convex form defined over this cone (see x 5) Our study of what we now call scaling dualities, and their algorithmic significance began in Kalantari [6], and was continued in [7] 11] We emphasize that the goal of the present paper is to present these significant dualities for the very special problems considered, and via an elementary proof. Also, to introduce two conceptually simple, but very capable polynomial time algorithms that are ....
....0 ; but not both. Remark 3. For i = 2 0 , Corollary 2.4 implies that either Karmarkar s canonical LP is solvable, or the potential function f (x) is unbounded from below; but not both. In fact Karmarkar s algorithm, 15] can be viewed as an algorithmic proof of this fact, see also Kalantari [6], 9] Another duality implied by this corollary is that either Karmarkar s canonical LP is solvable, or there there exists d 2 W K ffi such that P e;d D e c 0, but not both. This duality which implies Gordan s theorem gives rise to a simple variation of Karmarkar s algorithm (see Kalantari ....
B. Kalantari, Karmarkar's algorithm with improved steps, Math. Programming, 46 (1990) 73-78.
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