Algorithmic random duality theory – large scale CLuP

11/23/2020
by   Mihailo Stojnic, et al.
0

Based on our Random Duality Theory (RDT), in a sequence of our recent papers <cit.>, we introduced a powerful algorithmic mechanism (called CLuP) that can be utilized to solve exactly NP hard optimization problems in polynomial time. Here we move things further and utilize another of remarkable RDT features that we established in a long line of work in <cit.>. Namely, besides being stunningly precise in characterizing the performance of various random structures and optimization problems, RDT simultaneously also provided an almost unparallel way for creating computationally efficient optimization algorithms that achieve such performance. One of the keys to our success was our ability to transform the initial constrained optimization into an unconstrained one and in doing so greatly simplify things both conceptually and computationally. That ultimately enabled us to solve a large set of classical optimization problems on a very large scale level. Here, we demonstrate how such a thinking can be applied to CLuP as well and eventually utilized to solve pretty much any problem that the basic CLuP from <cit.> can solve.

READ FULL TEXT
11/23/2020

Rephased CLuP

In <cit.> we introduced CLuP, a Random Duality Theory (RDT) based algori...
11/23/2020

Sparse linear regression – CLuP achieves the ideal exact ML

In this paper we revisit one of the classical statistical problems, the ...
09/03/2019

Complexity analysis of the Controlled Loosening-up (CLuP) algorithm

In our companion paper <cit.> we introduced a powerful mechanism that we...
09/03/2019

Starting CLuP with polytope relaxation

The Controlled Loosening-up (CLuP) mechanism that we recently introduced...
04/05/2018

Structural cost-optimal design of sensor networks for distributed estimation

In this letter we discuss cost optimization of sensor networks monitorin...
09/03/2019

Controlled Loosening-up (CLuP) – achieving exact MIMO ML in polynomial time

In this paper we attack one of the most fundamental signal processing/in...
11/02/2020

AnyMOD.jl: A Julia package for creating energy system models

AnyMOD.jl is a Julia framework for creating large-scale energy system mo...