Solving classical optimization problems (continually updated)

This blog will talk about some of the classic problems need to opt for easy I / we can think of to optimize the way in deriving the corresponding formula and the need to optimize the future.

If even have derived a formula but is not it will not solve the awkward (do not know if can be converted into solving even the code can not write = =)

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Question 1

b Vector and Matrix A GIVEN, Minimize || b || Ax of- ² . (When A is greater than the number of rows of columns b, may not satisfy Ax-b = 0)

Based approach * = X (A ^T A) ^-1 A ^T B, which is inevitable can be solved.

 

Question 2

minimize ||Ax||², s.t. ||x||=1.

solution: let A = UDV^T, x = V_-1(the last column of V)