localSearchCircle.m

function x=localSearchCircle(funcToOptimize,proposalFunc,startingX,epsilon,lowerBoundOnX,upperBoundOnX,timeDelta,funcDelta)
% This general-purpose optimization routine aims to minimize funcToOptimize
% starting from the initial guess startingX, via proposals generated by
% proposalFunc (the two functions are specified via function handles). When
% optimizing a function whose inputs have lower and upper bounds, the
% proposal xp=proposalFunc(x) has all of its entries less than
% lowerBoundOnX rounded up to lowerBoundOnX, and all of its entries greater
% than upperBoundOnX rounded up to upperBoundOnX before funcToOptimize is
% evaluted on xp (these bounds can be -inf and +inf to make them effectively 
% ignored. The proposal is accepted if it improves the function value, or does
% not make it worse by more than epsilon. The routine terminates when timeDelta
% seconds have passed without the best value found so far of funcToOptimize
% improving by funcDelta.

x = startingX;
UB = upperBoundOnX;
LB = lowerBoundOnX;

while true
    t0 = now*60*60*24;
    t10 = t0;
    x_t0 = x; 
    
    while (abs(t10-t0)<=timeDelta)
        xp = proposalFunc(x);
        acceptBound = funcToOptimize(x,0) + epsilon;

        % to sanitise the input xp
        for i = 1:length(xp), xp(i) = min(max(xp(i), LB), UB); end
        f_xp = funcToOptimize(xp,0);
        
        
        if (f_xp <= acceptBound), x = xp; end
        
        t10 = now*60*60*24;
    end
    
    if (abs(funcToOptimize(x,0) - funcToOptimize(x_t0,0))<funcDelta)
        disp('we are done.');
        break;
    else
        disp('shalimar');
%         xcoords = x(1:2:19);
%         ycoords = x(2:2:20);
        UB = max(x);
        LB = min(x);
        
    end
            
end