I see that nonlinear programming entails nonlinear objectives with convex or linear constraints. Is there any theory/method to solve linear objective with nonconvex constraints and some convex constraints?
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Note that every optimization problem can be cast as a linear objective with non-linear constraints. – copper.hat Sep 26 '14 at 05:38
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So, you mean I could retrace the linear objective to something else and change the constraints to convex or linear ones? – sprajagopal Sep 26 '14 at 06:35
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No, what I meant was that if there was a significant advantage to dealing with linear objectives and non-convex constraints, then I suspect a related body of optimization would have arisen by now. Many years ago (in the context of $\max$ functions) I looked at something similar (over a small range of numerical optimizations) with no clear advantage/disadvantage. Don't think of the comment as definitive in any way! – copper.hat Sep 26 '14 at 06:40
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Oh, alright. That's a bummer. I felt like there was a standard approach to doing it. – sprajagopal Sep 26 '14 at 07:12