Talk:Convex optimization

message: The layout and presentation could be much better. I know it's a stub, but what little there is could at least be readable. 163.1.159.21 16:48, 14 May 2005 (UTC)
thread_title:  Layout 

message: The theory of convex optimization pertains to convex minimization, not maximization (apart from a maximum boundary principle). Maximizing (even quadratic QP) convex functions (on convex subsets) is NP hard. Shouldn't the title of the article be clarified to "Convex Minimization"?
Kiefer.Wolfowitz (talk) 14:32, 7 June 2009 (UTC)
thread_title:  "Convex minimization" would be better for this article 

message: Would somebody improve the illustration of the "problem hierarchy", please? 
Convex quadratic programming (QP) (with linear constraints) is more general than linear programming. 
I would not object to somebody changing the QP with Q constraints to simply QP (with linear constraints). Thanks. Kiefer.Wolfowitz (talk) 19:47, 7 January 2010 (UTC)
replies: text: I removed the still wrong diagram. Kiefer.Wolfowitz (talk) 16:39, 21 July 2010 (UTC)
thread_title:  Problem Hierarchy: QP covers LP (not shown in the illustration) 

message: The first sentence is gramatically wrong: "is focuses" -> "focuses"  —Preceding unsigned comment added by 139.179.161.17 (talk) 12:36, 28 February 2010 (UTC)
thread_title:  Grammar 

message: In the introductory section it is mentioned that
With recent improvements in computing and in optimization theory, convex minimization is nearly as straightforward as linear programming.
While that is certainly true in theory (existence of a rich duality theory and polynomial-time algorithms), I am not so sure to which extent this is true in practice. For linear programs, simplex and interior-point methods can solve problems with input size (nonzero entries on constraint matrix) on the order of millions on a desktop computer. But even for a well studied and highly structured class of convex optimization problems, namely, semidefinite optimization, current solvers do not fare very well even for problems with input size on the order of a few thousand nonzeroes. See the benchmarks at http://plato.asu.edu/bench.html.
It is obvious that this is not a fair comparison, given that the codes for LPs are obviously much more mature. However, semidefinite optimization solvers (as well as general convex optimization software) faces an apparently intrinsic problem of numerical stability.
If anybody else can confirm that I am not completely outdated about this, could you please add these remarks to the page, or let me know so that I can write the remarks myself? Thanks.
--Marcelkcs (talk) 15:20, 4 June 2011 (UTC)
thread_title:  Convex Optimization in practice 

message: *  Faigle, Kern, and another author treat convex maximization in the section on convex optimization. (I believe both Faigle and Kern have been elected to the governing board of MPS/MOS.)
* Boyd and Vandenberghe's Convex Optimization treats convex maximization in problem (8.16).
I trust the "factual accuracy" bs is over.  Kiefer.Wolfowitz 12:04, 3 February 2012 (UTC)
replies: text: No, unfortunately that does not settle the discussion (although it is more about terminology than factual accuracy). I don't understand what Boyd/Vandenberghe problem 8.16 has to do with this, and while the result on convex maximization can be mentioned further down in the article, I'm not convinced that referring to it as convex optimization represents the majority view. In case you are interested in Wikipedia policies, please have a look at WP:Wikipedia is not about winning and WP:UNDUE. I believe additional opinions on this from other people would be helpful. Isheden (talk) 21:15, 3 February 2012 (UTC)
replies: text: Let me know when you find a defined population from which a survey sample was taken, so I might try to understand what you're possibly thinking about with "majority view", an irrelevant concept on WP. I provided a reliable high quality source, which settles the matter of the sentence to which you have been objecting, according to WP policy.  Kiefer.Wolfowitz 04:40, 11 February 2012 (UTC)
thread_title: Restriction to "Convex optimization problem" considered harmful

message: I'm confused. The theory section states:
*if a local minimum exists, then it is a global minimum.
*the set of all (global) minima is convex.
*for each strictly convex function, if the function has a minimum, then the minimum is unique.
Technically you can have a set of one, but the middle line above loosely implies there can be multiple global minima, which is contradicted by the final statement. Can whatever is meant be better expressed please? Aarghdvaark (talk) 06:58, 30 August 2012 (UTC)
replies: text: The third bullet point applies only if it's a strictly convex function.  — Arthur Rubin  (talk) 07:58, 30 August 2012 (UTC)
thread_title:  Theory 

message: The applications section is quite poorly written. Almost all of its citations point to a single set of slides of Boyd et al., but those examples prove only that some problems can be modeled as convex optimization problems, not that convex optimization is actually used in practice to solve any of these problems. I've updated the phrasing appropriately in that section, but I would love it if someone could provide more concrete examples of convex optimization used in real world problems (not just in slides or academic papers).  — Preceding unsigned comment added by J2kun (talk • contribs) 19:35, 21 January 2024 (UTC)
thread_title:  Applications