Write down the directional derivatives of the univariate absolute-value function f(t) = |t-a| for a given...

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Write down the directional derivatives of the univariate absolute-value function f(t) = |t-a| for a given scalar a. Use the formula of these derivatives to write down the first-order necessary condition for optimality of the problem at a given vector x ER": minimize XERn n x¹Qx+\xi = αi\ i=1 for a given symmetric n × n matrix Q and scalars {a} 1. When is such a (necessary) condition sufficient for optimality (be specific)? Use the obtained condition to derive the optimal solution of the problem n n minimize ¦ Σca + Σαΐ ai, XERn i=1 i=1 where each coefficient c; is nonnegative (possibly zero). Is the optimal solution unique? Write down the directional derivatives of the univariate absolute-value function f(t) = |t-a| for a given scalar a. Use the formula of these derivatives to write down the first-order necessary condition for optimality of the problem at a given vector x ER": minimize XERn n x¹Qx+\xi = αi\ i=1 for a given symmetric n × n matrix Q and scalars {a} 1. When is such a (necessary) condition sufficient for optimality (be specific)? Use the obtained condition to derive the optimal solution of the problem n n minimize ¦ Σca + Σαΐ ai, XERn i=1 i=1 where each coefficient c; is nonnegative (possibly zero). Is the optimal solution unique?

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SOLUTION The univariate absolutevalue function is defined as ft ta To find the directional derivativ... View the full answer