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How can I code these functions (two objective optimization) using Matlab minimize f(x)=(x1-2)^2+(x2-5)^2 subject to g1=-x1-x2+10<=0 and g2=-2x1+3x2-10<=0
MATLAB has a TON of built in optimization functions. (You'll need the Optimization Toolbox.) Review the documentation and see which function best applies to your situtation. http://www.mathworks.com/help/optim/index.html