Talk:Linear-fractional programming

Category: Convex optimization

Linear fractional programs are pseudo-convex (Mangasarian) although not properly convex. However, since pseudo-convex programming lacks a category, I listed this in convex optimization. Kiefer.Wolfowitz (talk) 15:49, 9 October 2010 (UTC)[reply]

If there's no such category, then why don't you just create it? -- X7q (talk) 16:54, 9 October 2010 (UTC)[reply]

I cannot think of enough other "generalized convexity" topics. Kiefer.Wolfowitz (talk) 22:32, 9 October 2010 (UTC)[reply]

Minimization is canonical

For convex and quasi-convex problems, minimization is the canonical operation. Is there an objection to restoring minimization to the problem description~, as it used to be? (It is good that Isheden removed the inconsistencies, of course.) Kiefer.Wolfowitz 13:25, 21 May 2011 (UTC)[reply]

Most literature on fractional programming has considered the equivalent maximization of a quasiconcave function, which is often more natural in applications (such as maximizing an efficiency). On the other hand it is true that by convention convex optimization often focuses on minimization problems. I have nothing against including the minimization definition as well, but I would do it after the discussion of duality. One would have to search in literature to find the corresponding formulations in the minimization case. By the way, the article on linear programming also starts with the maximization case, and a potential article on nonlinear fractional programming would do so as well, because this convention has been used in almost all original references. Isheden (talk) 16:39, 21 May 2011 (UTC)[reply]

You make good points, and I applaud your efforts at consistency here. Kiefer.Wolfowitz 18:25, 21 May 2011 (UTC)[reply]