Question: Consider the minimization problemminxinR3f(x)where fis a convex function and the point xis such that gradf(x)=0. The eigenvalues of theHessian matrix grad2f(x*) are such that 1=0,2=1,3=3.

Consider the minimization problemminxinR3f(x)where fis a convex function and the point x*is such that gradf(x*)=0. The eigenvalues of theHessian matrix grad2f(x*) are such that 1=0,2=1,3=3. Then(a) the point x*is a local maximizer,(b) the point x*is a global minimizer,(c) the point x*is a stationary point but not enough information to decide(d) the point x*is neither minimizer nor maximizer.

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Question: Consider the minimization problemminxinR3f(x)where fis a convex function and the point x*is such that gradf(x*)=0. The eigenvalues of theHessian matrix grad2f(x*) are such that 1=0,2=1,3=3.

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Question: Consider the minimization problemminxinR3f(x)where fis a convex function and the point xis such that gradf(x)=0. The eigenvalues of theHessian matrix grad2f(x*) are such that 1=0,2=1,3=3.