Teorem V35 (1)

Question 1

Farkas’ Lemma for an inequality system (3.31)

Answer 1

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Question 2

Farkas’ Lemma (3.32 or 4.35; read proof in 10.10)

Answer 2

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Question 3

Characterization of convex functions in C1 (3.48)

Answer 3

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Question 4

The Fundamental Theorem of global optimality (4.3)

Answer 4

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Question 5

Necessary optimality conditions, C1 case (4.22)

Answer 5

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Question 6

Necessary and sufficient global optimality conditions (4.23)

Answer 6

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Question 7

The Separation Theorem (4.29)

Answer 7

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Question 8

Karush–Kuhn–Tucker necessary conditions (5.29)

Answer 8

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Question 9

Sufficiency of the Karush–Kuhn–Tucker conditions for convex problems (5.49)

Answer 9

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Question 10

Relaxation Theorem (6.1)

Answer 10

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Question 11

Weak Duality Theorem (6.5)

Answer 11

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Question 12

Global optimality conditions in the absence of a duality gap (6.8)

Answer 12

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Question 13

Existence and properties of optimal solutions (8.10)

Answer 13

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Question 14

Finiteness of the Simplex method (9.11)

Answer 14

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Question 15

Weak Duality Theorem (10.4)

Answer 15

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Question 16

Strong Duality Theorem (10.6)

Answer 16

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Question 17

Farkas’ Lemma (10.10)

Answer 17

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Question 18

Complementarity Slackness Theorem (10.11) - similar to 10.12

Answer 18

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Question 19

Complementarity Slackness Theorem (10.12) - similar to 10.11

Answer 19

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Question 20

Global convergence of a penalty method (13.3)

Answer 20

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