Weight minimization of a speed reducer

Nonconvex
1

please help me get started with this problem code.
or just write the code. :smiley: Also give me some link for cvx tutorials.
The objective of Golinski’s Speed Reducer problem is to find the minimum of a gear box volume f (and, hence, its minimum weight), subject to several constraints. There are seven design variables, x1 - x7 , which represent

x1 width of the gear face, cm
x2 teeth module, cm
x3 number of pinion teeth
x4 shaft 1 length between bearings, cm
x5 shaft 2 length between bearings, cm
x6 diameter of shaft 1, cm
x7 diameter of shaft 2, cm

Mathematically, the problem is specified as follows:
objective%20function

constraints
constraints.PNG355×518 8.45 KB

2

I doubt this is a convex problem. For instance g_5 does not look convex because that would have negative value in the Hessian for x_6. Right?

3

Except for some unfortunate terms, as @Erling pointed out, this would be a Geometric Program which CVX could handle. See http://cvxr.com/cvx/doc/gp.html and read https://web.stanford.edu/~boyd/papers/gp_tutorial.html for a more in depth understanding.

But his isn’t horseshoes, hand grenades, or nuclear weapons, so close doesn’t count.

The CVX Users’ Guide is the tutorial http://cvxr.com/cvx/doc/ . The are CVX examples at http://cvxr.com/cvx/examples/ as well as in this forum.

4

so is this non-convex?

5

You should prove to us that the problem is convex. That is your job but we think it is not convex.

7

i have re-written the problem by transforming it into convex MINLP. now this is convex and a geomtric program. kindly help with the code
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8

How did you transform this into a convex MINLP?

Please read the links in my previous post.

The terms in which the coefficient multiplying the variable powers are negative are not valid monomials, and therefore, this is not a valid generalized geometric program.

9

I think the only non-convexity is in the objective function. I believe the constraints have no more than one negative coefficient “monomial”, which can be moved to the RHS as a true monomial and be compliant with CVX’s Geometric Programming (gp) rules.

10

ill look into it. thanks alot