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Hello all,

Assume we have a sequence of quasiconvex quasiconcave functions (in $X$) denoted by $f_{i,j}(X)$ for $i,j = 1,\ldots,n$. Denote by $F(X)$ the $n\times n$ matrix whose $(i,j)$ entry is the function $f_{i,j}(X)$.

Assuming that $F(X)\succ0$, F\succ0$(positive definite for all$X$), I want to prove (or disprove) that the function$g(X)=a^TF^{-1}a$, where$a\in\mathbb{R}_+^{n\times 1}$, is quasiconvex. Someone have any idea? Thank you! Correction:$f_{i,j}(X)$are quasiconcave and not quasiconvex. Credit to Robert. 2 added 2 characters in body Hello all, Assume we have a sequence of quasiconvex functions (in$X$) denoted by$f_{i,j}(X)$for$i,j = 1,\ldots,n$. Denote by$F(X)$the$n\times n$matrix whose$(i,j)$entry is the function$f_{i,j}(X)$. Assuming that$F(X)\succ0$, I want to prove (or disprove) that the function$g(X)=a^TF^{-1}a$, where$a\in\mathbb{R}^{n\times a\in\mathbb{R}_+^{n\times 1}$, is quasiconvex. Someone have any idea? Thank you! 1 # Proving that a specific function is quasiconvex Hello all, Assume we have a sequence of quasiconvex functions (in$X$) denoted by$f_{i,j}(X)$for$i,j = 1,\ldots,n$. Denote by$F(X)$the$n\times n$matrix whose$(i,j)$entry is the function$f_{i,j}(X)$. Assuming that$F(X)\succ0$, I want to prove (or disprove) that the function$g(X)=a^TF^{-1}a$, where$a\in\mathbb{R}^{n\times 1}\$, is quasiconvex.

Someone have any idea?

Thank you!