Computable bounds on parametric solutions of convex problems (Q1106102)

For the parametric convex problem \(\min_{x}f(x,\epsilon)\), such that \(x\in R(\epsilon)\), where \(R(\epsilon)=\{x\in E^ n;\) \(g_ i(x,\epsilon)\geq 0\), \(i=1,...,m\), \(h_ j(x,\epsilon)=0\), \(j=1,...,p\}\), \(\epsilon\in E^ r\) is the vector of parameters, \(f: E^ n\times E^ r\to E^ 1\) is \(C^ 2\) and convex in \((x,\epsilon)\), \(g_ i: E^ n\times E^ r\to E^ 1\) are \(C^ 2\) and concave in \((x,\epsilon)\) and \(h_ j: E^ n\times E^ r\to E^ 1\) are affine in \((x,\epsilon)\), the authors obtain computable upper and lower bounds on the optimal solution.