Lecture 1-Convex Optimization (Stanford) Question

Question 1

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The symbol x⋆ usually denotes

• a feasible point
• the optimal value of the problem
• a solution

Question 2

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Least squares is a special case of convex optimization.

• true
• false

Question 3

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Almost any problem you'd like to solve in practice is convex.

• true
• false

Question 4

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Convex optimization problems are attractive because they always have a unique solution.

• true
• false

Question 5

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In device sizing, the problem is to design a device that minimizes power consumption subject to the total area not exceeding 50, along with some timing and manufacturing constraints. Suppose four candidate designs meet the timing and manufacturing constraints and have power and area listed in the table below.

Design B is better than design A.

• true
• false

Design C is better than design A.

• true
• false

Design D cannot be optimal.

• true
• false

Question 6

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Local optimization

• is currently illegal in 17 states
• can be quite useful in some contexts, and therefore is widely used
• can't guarantee finding a (global) solution.

Question 7

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Convex optimization has become popular

• because most convex problems have analytical solutions.
• because the mathematics is elegant.
• due to development of effective solution algorithms and powerful computers to run them.
• because you don't need to know much to use it.
• because convex problems always have well-defined unique solutions.

 

Answer

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Q1 Ans) a solution

Q2 Ans) true

Q3 Ans) false

Q4 Ans) false

Q5 Ans) false, false, true

Q6 Ans) can be quite useful in some contexts, and therefore is widely used, can't guarantee finding a (global) solution.

Q7 Ans) because the mathematics is elegant., due to development of effective solution algorithms and powerful computers to run them.