On a Class of Optimization Problems with No 'Effectively Computable' Solution

13 Pages Posted: 22 Nov 2015

See all articles by Misha Gavrilovich

Misha Gavrilovich

National Research University Higher School of Economics

Victoria Kreps

National Research University Higher School of Economics

Date Written: November 20, 2015

Abstract

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

Suggested Citation

Gavrilovich, Misha and Kreps, Victoria, On a Class of Optimization Problems with No 'Effectively Computable' Solution (November 20, 2015). Higher School of Economics Research Paper No. WP BRP 112/EC/2015, Available at SSRN: https://ssrn.com/abstract=2693527 or http://dx.doi.org/10.2139/ssrn.2693527

Misha Gavrilovich (Contact Author)

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

Victoria Kreps

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

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