Let QMnn (R) and c ER. Consider the quadratic function f: R R given by f(x)...
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Let QMnn (R) and c ER". Consider the quadratic function f: R" R given by f(x) = 2xQxcx. (a) Write down the first order necessary condition for the unconstrained problem minimise f(x). Under what conditions does a stationary point exist? (b) Under what conditions on Q does a local minimiser exist? (c) Under what conditions on Q does f have a stationary point but no local maxima or minima? Let QMnn (R) and c ER". Consider the quadratic function f: R" R given by f(x) = 2xQxcx. (a) Write down the first order necessary condition for the unconstrained problem minimise f(x). Under what conditions does a stationary point exist? (b) Under what conditions on Q does a local minimiser exist? (c) Under what conditions on Q does f have a stationary point but no local maxima or minima?
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