![]() ![]() I don't need a precise solution but rather a numerical approximation. ![]() The code is something like this: syms y1 y2 圓 y4 z1 z2 The equations are correct and I'm sure there are solutions to it as I can solve them with Mathematica but I'd like to be able to solve them in matlab so that I can write my code in there instead of Mathematica. I've tried to use vpasolve and solve but the code doesn't bring any solution. Whether it has been done already in a standard package, I cannot tell.I'm trying to solve a set of quadratic equations for a code I'm working on. However, this is quick enough and easy to program. That would require tracing the degenerate plane. The catch is that the Lagrange problem degenerates when you have multiple solutions in the original problem, so you'll easily determine the value of the minimum of $F(z)$ but not immediately the value of $z$. ![]() Moreover, the global minimum in the original problem corresponds to $q$ such that $(A(q)^B(q),B(q))$ are convex, so the methods of convex optimization work. (note that $c$ does not depend on $q=(q_n)$!) The Lagrange multiplier theorem tells that if you have a local minimum of $F(z)$ under the conditions $G_n(z)=0$, then we can find $q_n\in\mathbb R$ such thatį_q(z)=F(z)+\sum_n q_n G_n(z)=(A(q)z,z)-2(B(q),z)+cĪttains a global minimum at the same point. Set the problem asĪnd consider both the objective and the conditions as quadratic forms of $z=(x,y)$. ![]() Suppose you want to minimize $\sum_n Q_n(x)^2$ where $Q_n$ are quadratic forms. There is one fancy way specific for the quadratics. So, is there a free math tool (like Sage) which can minimize things for me (and be certain that no other point is better within some tolerance)? I'm open to theoretical advice, but feel like the options will all look like brute force. I'm thinking there might be some software tool that considers the "terrain" smartly and is locally minimizing on many global fronts.or maybe that is impractical. This example probably actually has a solution where all equations are zero, but I also have cases which have no zero solution, so I'd rather not do the "repeatedly eliminate variables and solve for the quadratic root" approach (also, this approach takes too long is there even any machine which could find a full zero for these equations within 10 minutes?). Syntax S solve (eqn,var) S solve (eqn,var,Name,Value) Y solve (eqns,vars) Y solve (eqns,vars,Name,Value) y1.,yN solve (eqns,vars) y1.,yN solve (eqns,vars,Name,Value) y1. For example, I am looking to make the 6 equations below as "small" as possible (a-j are unknown real numbers). I have many polynomial equations in many variables which I want to jointly minimize (in a mean square sense, but you could pick a different reasonable measure which favors anything where all quantities go to zero). ![]()
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