On a Class of Optimization Problems with No 'Effectively Computable' Solution
13 Pages Posted: 22 Nov 2015
Date Written: November 20, 2015
It is well-known that large random structures may have non-random macroscopic properties. We give an example of non-random properties for a class of large optimization problems related to the computational problem MAXFLS^= of calculating the maximal number of consistent equations in a given overdetermined system of linear equations. A problem of this kind is faced by a decision maker (an Agent) choosing the means to protect a house from natural disasters. For this class we establish the following. There is no “efficiently computable” optimal strategy for the Agent. When the size of a random instance of the optimization problem goes to infinity the probability that the uniform mixed strategy of the Agent is ε optimal goes to one. Moreover, there is no “efficiently computable” strategy for the Agent which is substantially better for each instance of the optimization problem.
Keywords: optimization, concentration of measure, probabilistically checkable proofs
JEL Classification: C61
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