Solving systems of equations in Matlab

How to solve these equations in MATLAB?


Lines 1 and 3 independent from lines 2 and 4, and can be solved easily.

Regarding lines 2 and 4, you can solve them using genetic algorithms with gamultiobj (which give a set of approximate solutions, aka. Pareto frontier):


FitnessFunction = @objectives;
numberOfVariables = 2;
options = gaoptimset('Generations', 100, 'PopulationSize', 100);
[X,FVAL,EXITFLAG,OUTPUT] = gamultiobj(FitnessFunction,numberOfVariables,[],[],[],[],[],[],options)


function y = objectives(x)
   w = x(1);
   y = x(2);
   y(1) = abs(2*w*y-2*w+1);
   y(2) = abs(2*w+y^2-2*y-1);

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