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Introduction to convex optimization

Least squares is a special case of convex optimization.
  1. True.
    Correct!
  2. False.
    Incorrect.
By and large, convex optimization problems can be solved efficiently.
  1. True.
    Correct!
  2. False.
    Incorrect.
Almost any problem you'd like to solve in practice is convex.
  1. True.
    Incorrect. Most convex optimization problems are not convex. Nevertheless, many problems of interest can be solved via convex optimization.
  2. False.
    Correct!
Convex optimization problems are attractive because they always have a unique solution.
  1. True.
    Incorrect. They do not always have a unique solution, and even when they do, this is not of primary importance.
  2. False.
    Correct!

In a device sizing problem the goal is to minimize power consumption subject to the total area not exceeding 50, as well as some timing and manufacturing constraints. Four candidate designs meet the timing and manufacturing constraints, and have power and area listed in the table below. \[ \begin{array}{lll} {\rm Design} & {\rm Power} & {\rm Area} \\ \hline {\rm A} & 10 & 50 \\ \hline {\rm B} & 8 & 55 \\ \hline {\rm C} & 10 & 45 \\ \hline {\rm D} & 11 & 50 \\ \hline \end{array} \]
Design B is better than design A.
  1. True.
    Incorrect. Device B is infeasible and device A is feasible.
  2. False.
    Correct!
Design C is better than design A.
  1. True.
    Incorrect. Both are feasible and achieve the same objective value, so they are equally good.
  2. False.
    Correct!
Design D cannot be optimal.
  1. True.
    Correct!
  2. False.
    Incorrect. Design A is also feasible and achieves a better objective value (lower power consumption).

Very roughly, how long would it take to solve a linear program with 100 variables and 1000 constraints on a computer capable of carrying out a billion floating point operations per second (1 gigaflop)?
  1. Microseconds.
    Incorrect.
  2. Milliseconds.
    Correct!
  3. Seconds.
    Incorrect.
  4. Minutes.
    Incorrect.

Local optimization
  1. can be quite useful in some contexts, and therefore is widely used.
    Correct!
  2. is currently illegal in 17 states.
    Incorrect.
  3. can't guarantee finding a (global) solution, and so is not widely used.
    Incorrect. Though they can't guarantee finding a global solution, they are nevertheless useful and widely used.