Dual infeasibility SOSTOOLS - Polynomial optimization relaxed to SDP
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So, I have a semialgebraic set in the 2-d space defined by the polynomial inequalities F1(x0,y0)>=0 and F2(x0,y0)<=0. If we denote as (x0,y0) the points on the 2-d plane, I want to find the maximum y0 component among all of the set's points. I know that this problem can be relaxed to an SDP. However, the following code gives me dual infeasibility:
Program1 = sosprogram([x0;y0], y0);
Program1 = sosineq(Program1, F1);
Program1 = sosineq(Program1, -F2);
Program1 = sossetobj(Program1, y0);
options.solver='sdpt3';
Program1 = sossolve(Program1, options);
sosgetsol(Program1, y0)
Any help?
P.S. F1 and F2 are, indeed polynomial, and the set is indeed bounded. I mean there is nothing wrong with the code above of the given one, evaluating the functions
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