As an electrical engineer, I have been studying convex optimization for a while. During my study, I see that most textbooks claim that both second-order cone programs (SOCP) and geometric programs (GP) can be solved effectively with a modern solver. However, I cannot find any document that compares them. Hence, is SOCP harder than GP. Furthermore, is there anyway to come up with a Big O complexity to measure the difficulty of solving them in terms of the number of variables and constraints?
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$\begingroup$ Aren't you conflating problems and algorithms? $\endgroup$– Rodrigo de AzevedoCommented Dec 12, 2023 at 9:54
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$\begingroup$ Oh my bad for not being clear enough. What I really want to said is on the problem aspect. As they are both non linear problem, I dont know which problem is harder ? $\endgroup$– Tuong Nguyen MinhCommented Dec 12, 2023 at 10:17
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1$\begingroup$ A problem is a collection of instances. There are different algorithms for LP, for example, and they don't have the same worst-case complexity $\endgroup$– Rodrigo de AzevedoCommented Dec 12, 2023 at 10:20
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