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be defined Proposition 2.16. Let the inequality constrained problem by a symmetric matrix A E Rnxn, a constraint matrix B E Rmxn, and vectors b, c. Let C denote the cone of recession directions of the nonempty feasible set 1. Then the following statements hold: (i) If problem (2.50) has a solution, then dr Ad> 0 for d EC and db≤0 for de Cn KerA. (ii) If (2.55) holds and f is convex, then problem (2.50) has a solution. (iii) If f is convex and (x,x) and (y) are KKT couples for (2.50), then x-ye KerA and - KerBT.

be defined Proposition 2.16. Let the inequality constrained problem by a symmetric matrix A E Rnxn, a constraint matrix B E Rmxn, and vectors b, c. Let C denote the cone of recession directions of the nonempty feasible set 1. Then the following statements hold: (i) If problem (2.50) has a solution, then dr Ad> 0 for d EC and db≤0 for de Cn KerA. (ii) If (2.55) holds and f is convex, then problem (2.50) has a solution. (iii) If f is convex and (x,x) and (y) are KKT couples for (2.50), then x-ye KerA and - KerBT.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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it's  cs question dont reject if you dont know ans.

Proposition 2.16. Let the inequality constrained problem be defined by a symmetric matrix A E Rnxn, a constraint matrix B E Rmxn, and vectors b, c. Let C denote the cone of recession directions of the nonempty feasible set 21. Then the following statements hold: (i) If problem (2.50) has a solution, then dT Ad 20 for d EC and db≤0 for de Cn KerA. (ii) If (2.55) holds and f is convex, then problem (2.50) has a solution. (iii) If f is convex and (x,x) and (y,) are KKT couples for (2.50), then x-ye KerA and - KerBT. 1
Transcribed Image Text:Proposition 2.16. Let the inequality constrained problem be defined by a symmetric matrix A E Rnxn, a constraint matrix B E Rmxn, and vectors b, c. Let C denote the cone of recession directions of the nonempty feasible set 21. Then the following statements hold: (i) If problem (2.50) has a solution, then dT Ad 20 for d EC and db≤0 for de Cn KerA. (ii) If (2.55) holds and f is convex, then problem (2.50) has a solution. (iii) If f is convex and (x,x) and (y,) are KKT couples for (2.50), then x-ye KerA and - KerBT. 1
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