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Consider the following sum of fractional functions optimization problem $$ \begin{array}{l} \mathop {\min }\limits_{\bf{x}} \,\,\,\sum\limits_{i = 1}^p {\frac{1}{{{\bf{a}}_i^T{\bf{x}} + {b_i}}}} \\ subject\,\,to:\,\,\,{\bf{x}} \in X \end{array}$$

where ${{\bf{a}}_i^T{\bf{x}} + b}>0$ and $X$is a non empty compact convex set. How can I solve the optimization problem?

AlexR
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user51780
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  • [tag:fractional-calculus] is a completely different matter, hence I removed the tag. For the problem: What else do you know about $X$? Is the objective function self-concordant on $X$? If so, you can apply standard convex optimization theory. – AlexR Aug 22 '15 at 20:39
  • What do you mean about the objective function is self-concordant on X?l am looking for an algorithm to solve the problem with Cvx because Cvx can not solve the problem! – user51780 Aug 25 '15 at 08:14
  • This question is duplicated, see: https://math.stackexchange.com/questions/1417537/minimization-of-sum-of-linear-fractional-functions – The Pheromone Kid Apr 05 '19 at 09:24

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