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4 votes

Nonconvex optimization problem

In general, you can show that a class of problems is NP-Hard by taking a known NP-hard problem and reducing it to a problem in your class (being careful that size of the problem does not increase too …
Brian Borchers's user avatar
2 votes
Accepted

A non-convex quadratically constrained quadratic program

It's helpful if you cite the paper in which you saw something that you're asking a question about- we could provide a better answer if we knew where the question came from. First, assume without lo …
Brian Borchers's user avatar
2 votes
Accepted

Solving a non-convex quadratically-constrained quadratic program

Branch-and-Bound can be used to solve problems like this, but it's an exponential time algorithm that is not practical for large instances of the problem. What is $n$, the dimension of the $x$ vector …
Brian Borchers's user avatar
5 votes

Projected gradient descent for non-convex optimization problems

First, I'm assuming that your nonconvex feasible set $D$ is a subset of some larger convex set $C$ on which the objective function $f(x)$ is defined. It doesn't really make sense to talk about $f(x)$ …
Brian Borchers's user avatar