Hard Thresholding is Non-Convex

Hard Thresholding is Non-Convex.carbide.md

Hard Thresholding is Non-Convex

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cell0.js

var lam = 1.75;
var sigma    =0.55;
var varsigma = 0.70;
var theta    = 1/(1 + sigma**2);
var vartheta = 1/(1 + varsigma**2);


var MSE0   = 6;
var MSE1   = 3 * (1 - theta**2) + 3;
var MSE2   = 1 + 4 * (1 - vartheta**2) + 1;
var MSE3   = 3 + 3 * (1 - theta**2);
var MSE12  = (1-theta**2) + 2*([1-theta] - [0.5*(2-theta)*vartheta])**2 + 2*(1-vartheta**2) + 1;
var MSE13  = 3*(1-theta**2) + 3*(1-theta**2);
var MSE23  = 1 + 2*(1-vartheta**2) + 2*([1-theta] - [0.5*(2-theta)*vartheta])**2 + (1-theta**2);
var MSE123 = (1-theta**2) + 4*([1-theta] - [0.5*(2-theta)*vartheta])**2 + (1-theta**2);



var PEN0   = 0;
var PEN1   = lam;
var PEN2   = lam;
var PEN3   = lam;
var PEN12  = 2*lam;
var PEN13  = 2*lam;
var PEN23  = 2*lam;
var PEN123 = 3*lam;



var VAL13  = MSE13 + PEN13;
var VAL12  = MSE12 + PEN12;
var VAL2   = MSE2 + PEN2;
var VAL1   = MSE1 + PEN1;
var VAL123 = MSE123 + PEN123;

VAL13 < VAL12;
VAL2 < VAL1;
VAL2 < VAL12;
VAL2 < VAL123;
VAL2 < 6;


var CORR12 = Math.sqrt(theta*vartheta/3);