KingCobra Code-svn

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Convex Optimization - Pricing Computation - 30 August 2017
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(*) Prices of Goods/Services have been computed explicitly from Karush-Kuhn-Tucker Conditions (1,2,3 and especially 4)
(*) References:
- Pages 106-108 of http://www.cs.cmu.edu/~sandholm/cs15-892F13/algorithmic-game-theory.pdf)
- KKT conditions and Conic Optimization- https://arxiv.org/pdf/1312.3039.pdf
(*) logs committed to testlogs/

Updated KingCobra Design Document

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Convex Optimization update - 29 August 2017
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(*) Removed hardcoded variable values in objective and constraints
(*) In the context of pricing, ECOS Error Metrics print the matrices of market clearing prices for goods
(Reference - pages 3072 and 3073 of https://web.stanford.edu/~boyd/papers/pdf/ecos_ecc.pdf - KKT conditions in ECOS solver)

Updated KingCobra Design Notes

(*) Verbose set to True for printing Splitting Conic Solver progress information
(*) logs committed to testlogs/

Updated KingCobra Design Notes

(*) import dccp has been added
(*) DCCP is the recent advancement and generalization of DCP for convex-concave programs
(*) method='dccp' has been added as parameter to solve()
(*) Objective function has been changed to log() from logistic() - curvature is concave which is in conflict with definition of
eisenberg-gale convex program in textbooks. Reason for this contradiction is unknown.
(*) But DCCP overcomes the DCP limitation and solve() prints converged solutions for objective functions
(*) logs have been committed to testlogs/

Updated KingCobra Design Notes

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CVXPY implementation for Eisenberg-Gale Convex Program
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(*) First commits for Convex Optimized Market Equilibrium Prices
(*) Imports CVXPY Convex Program solver
(*) Objective function is a logistic variant of Eisenberg-Gale Convex Program i.e uses money * log(1+e^utility) instead of
money * log(utility) because of curvature error (log is error flagged as concave and logistic is convex per:
http://www.cvxpy.org/en/latest/tutorial/functions/index.html#vector-matrix-functions)
(*) Formulates constraints and objective functions based on http://www.cs.cmu.edu/~sandholm/cs15-892F13/algorithmic-game-theory.pdf - Page 106 and Equation 5.1
(*) But, For all installed solvers ECOS, ECOS_BB, SCS, LS solved convex program prints value as None despite all constraints and objective functions
being convex. Also is_dcp() prints "not a disciplined convex program". Logs in testlogs/.
(*) Obviously it should have worked. Therefore this is only a partial implementation commit.
(*) This implementation uses numpy randomly initialized arrays for Money each buyer has and per-good utility(happiness) each buyer has.
(*) Replacing money with perceived merit values translates this Market Equilibrium - Intrinsic Value versus Market Price - to Merit
Equilibrium - Intrinsic Merit versus Perceived Merit. This has been already described in NeuronRain AsFer Design Documents:
- http://sourceforge.net/p/asfer/code/HEAD/tree/asfer-docs/AstroInferDesign.txt and
- https://github.com/shrinivaasanka/asfer-github-code/blob/master/asfer-docs/AstroInferDesign.txt

Updated KingCobra Design Notes