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I'm assuming you believe that $\hom_{\mathrm D(k)}(\mathrm R f_\ast \mathcal F[i],k)=\hom_{\mathrm D(k)}(k,\mathrm R f_\ast \mathcal F[i])^\vee$. Now let $f:\mathcal A\to \mathcal B$ be a left-exact functor on abelian categories. It is well-known (see Corollary 10.5.7 of Weibel, for example) that there are natural isomorphisms $\mathrm H^i(\mathrm R ...


Got a hint to solve $\sum^N_{i=1} \alpha_i(\boldsymbol{x}_i - \boldsymbol{S})^T(\boldsymbol{x}_i - \boldsymbol{S})$ instead.


I have designed the dual problems according to the attached table. First dual problem $\begin{gather} \color{blue}{min}\hspace{.1cm} \ 5y_1+3y_2\\ s.t.\hspace{.1cm} \ \ y_1-y_2= 5\\ \ \ 2y_1+5y_2 \ge 6\\ y_1 \ \text{free}, \ y_2 \le 0 \end{gather}$ Second dual problem $\begin{gather} \color{blue}{min}\hspace{.1cm} \ 5y_1+6y_2\\ s.t.\hspace{.1cm} \ \ ...

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