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
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
Problem 1PE
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3631bf58-b64c-4a2e-afc3-e111390eadc6%2Ffd3a890b-7bb5-4760-9fcf-ace23eca30f9%2Fgxqemf_processed.jpeg&w=3840&q=75)
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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