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What kinds of complexity cause inefficiency for solving convex optimization problems?


These constraints are for guaranteeing that we can find global minima? What if we actually preferred to find a local minima (like in the example of protein folding on slide 10)? Are the constraints on the types of domains/objectives more or less strict than these, or are they different altogether?


Is determining convexity always efficient(can be done in polynomial time)?


What is an example of convex problem that is not quite efficient? Is the positive semidefinite or indefinite case (on the next slide) an example?


How would we check if something is convex without knowing exactly what function it follows.


What is the application of convex optimizations?


When you say that convex optimization doesn't depend on initialization, I assume you mean that you will eventually get a correct answer no matter which starting point you choose. But is the choice of initialization still important to help you converge to the minimum faster, or does this not really matter?


Could you give some examples that needs convex optimization in the graphics domain?


What is weak convexity?


Can we always treat non convex problems in cg as multiple convex problems? What are some examples that this might fail to work?


Is it possible to transform, apply constraints, or use other methods to make the convexity of a domain stronger?


Is gradient descent the main method in which convex optimization problems are solved, or are there other feasible approaches?


How to transform nonconvex objective/domains to convex ones?


Is there any way to limit the domain x of a nonconvex objective so that only a convex objective subsegment is considered?


How about complex plane? Is this still hold in the complex plane?


If one has a convex function but a non-convex domain, are there ways to restrict the problem to convex subsets to get approximate solutions?


When are complex problems not efficient in graphics?


What is the difference between strong and weak convexity and how does that affect how we can solve the problem?