I am trying to solve the following binary quadratic program. $$ \min_{\Delta} \Delta^T H \Delta + c^T\Delta \\ \text{Such that:} ~~~\Delta\in \{0,1\}^n ~~\text{and}~~ \sum_{i=1}^n \Delta_i \leq \Gamma $$ where $H$ is not a positive semidefinite matrix (and hence the minimization problem is not convex) and $\Gamma$ is a fixed natural number less than $n$. I […]

I would like to solve the following optimisation problem: $$\text{minimize} \quad x’Ax \qquad \qquad \text{subject to} \quad x’Bx = x’Cx = 1$$ Where $A$ is symmetric and $B$ and $C$ are diagonal. Does anyone have a suggestion for an efficient way of solving this? Thank you.

Let’s say we are given a race track, which may be described as a closed curve of given width (it may differ along the curve). My task is to implement an algorithm which finds two kinds of trajectories for the car. The first one is the shortest path, i.e. such closed curve contained in the […]

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