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I have an optimization function which contains an objective function which contains sum of decision variables, division of sum of decision variables and also product of sum of decision variables. The constraints include equality constraints of the norm and also some inequality constraints as well. I have been so confused over time which optimization technique to use and I want to learn that accordingly. I want to know what is the difference between non-linear optimization and convex optimization. Is convex optimization used to solve non-linear problems or techniques for optimization for non-linear are different. What kind of optimization would be suited to the problem which I am facing ?

Waqas
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  • Non-linear optimization is the most general problem, as there are no constraints on the objective function and domain. Non-linear methods are also able to solve convex problems, but they will do it less efficiently, not taking advantage of the convexity properties. Convex methods can only be used on convex functions/domains, they are more specialized. You need to check if your specific problem fulfills the convexity conditions. –  Sep 30 '14 at 07:24
  • In a book of non-linear optimization, I have read different sections for un constrained and constrained optimization. I am trying to figure out what I need to do to establish whether I have to use non-linear or it can be solved with convex optimization. Or should I try to transform my problem in to a convex optimization problem. – Waqas Sep 30 '14 at 07:29
  • Caution, mind a possible confusion. "there are no constraints on the objective function" is not referring to contrained/unconstrained optimization, it is referring to the fact that the objective function may have specific properties like convexity. –  Sep 30 '14 at 07:33
  • If your problem is inherently convex or you can turn it to a convex one, it should be better to solve it using convex methods. –  Sep 30 '14 at 07:34

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