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You should look into the topic of "parameteric linear programming". In certain situations where the problem data vary linearly with parameters, you can derive formulas for the optimal solution and op …

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 …

In using least squares, you normally want the residuals from the various equations to be indpendent of each other. If your $q_{i}$ vectors are imprecise measurements, then this will introduce correla …

The real issue here is the constraint $\sum_{i} x_{i}1_{x_{i}>a} < b $ whose left hand side has horrible discontinuities. Rather than using a solver designed for problems with continuous variable …

It isn't clear from your posting whether you're trying to understand: Why the inequalities generated by the Sherali-Adams procedure are valid? or Why the procedure is complete in the sense that af …

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 …

As mentioned by another poster, the work of Nesterov and Nemirovski summarized in Interior-Point Polynomial Algorithms in Convex Programming showed that many convex optimization problems (including li …

I'll assume in my answer that you're using the convention that the primal problem is: $\max tr(CX) $ subject to $tr(A_{i}X)=b_{i}\;\; i=1, 2, ..., m$ $X \succeq 0$ where $X$ is an $n$ by $n$ sym …

Some books to start with for background reading would include: Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2003. Y. Nesterov and A. Nemirovsky, Interior Poin …

Your notation is somewhat confusing, in that you apply the subscript $i$ to $w$, and have a vector $w_{i}$, but don't use $i$ in any meaningful way in your problem. I'm going to take the liberty of …

No, that's not quite the generalization that you'll get when you extend the Schur complement theorem for positive definite matrices to negative definite matrices. Try using the fact that a matrix $X$ …

As in your previous question, this is a nonconvex optimization problem, so it won't be LP, SOCP, or SDP representable. You've only got a 21 dimensional problem, and the constraint functions have ea …

Unfortunately, this problem can't be represented by an LP, since your feasible region is in general nonconvex, and the feasible region of an LP (being the intersection of a bunch of half spaces) is al …

There are a number of widely used primal--dual interior point codes for SDP, including SeDuMi, SDPA, SDPT3, and CSDP. Of these, SeDuMi approaches this problem by using the self dual embedding, while …

Many (but not all) problems involving the eigenvalues of a graph are convex optimization problems that can be formulated as semidefinite programming problems. There are a number of "tricks" that you …