non-convex | contained implementation of non-convex optimization | Math library

Update: potential answer added.

I am trying to write a multiobjective pyomo optimization script that optimizes the battery capacity and operational schedule based on minimizing the cost. It is supposed to answer what is the optimal size of a battery that reduces the electricity bill by charging when prices are low and discharging when prices are low, e.g. minimizing grid purchases when prices are high. I have been able to optimize the operational schedule when the capacity of the battery is given. However, I am having issues implementing the capacity optimization. The hourly load profile (electricity consumption) for a building and hourly electricity purchase prices are given (load[i] and price[i]). The cost is a constant with price per kwh for battery capacity.

I am using the ipopt solver.

I have tried different approaches. The first one does provide an optimal schedule and a capacity. However, I am unsure if this is the correct approach for optimal capacity since it is implemented in the same objective function that minimizes cost of battery + cost of purchased electricity - cost of energy discharged from battery.

I'm trying to solve an optimization question similar to the toy example described below. As noted in the comment, my current implementation with scipy is too slow and doesn't seem to converge. How do I get a decent solution? You can use scipy, mystic, or whatever library as you see fit.

Note that I don't need a global minimum, and the search can stop as soon as loss(X) <= 1. The real-world objective is mostly written in SQL and thus absurdly slow, so I also want the optimization to terminate when loss has been evaluated ~200 times. (This is not a hard requirement, you can also terminate after the optimization has been running for say 5 minutes.)

While this question resembles Minimizing non-convex function with linear constraint and bound in mystic, it's definitely not a duplicate. These two questions aren't even treating the same objective.

I have a non-convex quadratic optimization problem of type

x' * B * x,

where all entries of x are between 0 and 1 and the sum of all entries is identical to 1.

In scipy.optimize I would try to solve this optimization problem via

I am new to Gurobi (and solvers in general) and have set up a quadratic non-convex optimization problem by hand in LP file format. The following is a small example that is representative of much larger problems that I will be solving. Gurobi gives "Model is infeasible or unbounded" for this problem. I am setting params.NonConvex = 2 in the model to select the non-convex quadratic solver.

I do understand that having product terms of binary variables is bad form and will be fixing that once I can solve this issue.

I'm currently writing an y-monotone sweep line algorithm to triangulate non-convex polygons. The first step to achieve this is to make the polygon y-monotone.

Pseudocode of MakeMonotone from the book "Computation Geometry by Mark de Berg" (https://archive.org/details/computationalgeo00berg):

Now to my question:

In that book and all other websites I found, there is no explanation how to exactly sort the edges in the mentioned "binary search tree T". The only thing mentioned in the referenced book is "The left-to-right order of the leaves of T corresponds to the left-to-right order of the edges". But by what properties/attributes the edges are ordered in that tree? It's also unclear to me, how exactly an edge should be represented in the binary tree (start point? end point? combination of both?).

My most naive approach would be to find out for all edges in T the intersection with the sweep and line and the calculate which of them is closest to the current verex. But given that in every book/university slides, the inner working of T is not explained further, it must be way easier.

The binary search tree should support the following operations:

• insert a new edge
• find edge to the left of the vertex currently on the sweep line
• remove an edge

From the answer to this question here 3 years ago it seems, this is not possible. The Gurobi documentation is not clear ro me:

the model argument state

quadcon (optional)
...
The optional sense string defines the sense of the quadratic constrint. Allowed values are <, = or >. If not present, the default sense is <. It is stored in model$quadcon[[i]]$sense.

constraints state

Quadratic Constraints
...
Quadratic equality constraints are always non-convex; they will give a GRB_ERROR_QCP_EQUALITY_CONSTRAINT error with default settings.
[...] If you set the NonConvex parameter to 2, however, then Gurobi will accept arbitrary quadratic constraints and attempt to solve the resulting model.

But NonConvex throws an Error 10007: Unknown parameter: 'NonConvex' in R.
Any help is appreciated, a reproducible example can be found below:

I have been training with the following programming exercise: Circles in Polygons. The statement is:

You are the owner of a box making company.

Your company can produce any equal sided polygon box, but plenty of your customers want to transport circular objects in these boxes. Circles are a very common shape in the consumer industry. Tin cans, glasses, tyres and CD's are a few examples of these.

As a result you decide to add this information on your boxes: The largest (diameter) circular object that can fit into a given box.

I have found the following formula:

Taken from: https://www.mathopenref.com/polygonincircle.html

So to calculate the diameter of the largest incircle we have:

sideLength / tan(180/numberOfSides)

I have written the following code:

I have a matrix A of size nx2 collecting 2D points in Matlab. It is uploaded here (unfortunately, I cannot reproduce it with a simple code).

When I plot them using scatter I get the following picture, where

• The black region is non convex

• The boundary of the region is very "unsmooth", the dots of the scatter are quite visible along the boundary.

scatter(A(:,1), A(:,2), 50,'k', 'filled') xlim([-4 4]) ylim([-4 4])

Question: I would like to know whether there is a way to smooth the boundary of the region. I thought about using patch, but given that the region is non-convex, I don't know how to get its vertices. I also tried to increase the size of the scatter dots but the result is even worse. Are there some solutions?

I am using MINLP with NEOS solver, my problem is non-convex and I get this