Solve Algebraic Riccati Equation in R - r

I know that it's quite simple to solve the equation in Matlab. But is there a way to solve it in R as well? I need it for my Kalman filter implementations.

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How to use `cplexAPI` to solve quadratic programs/linear programs with quadratic constraints?

I am trying to use cplexAPI to solve quadratic programs or linear programs with a quadratic constraint.
While it seems to be pretty straightforward to use cplexAPI to solve linear programs (with the vignette at https://cran.r-project.org/web/packages/cplexAPI/vignettes/cplexAPI.pdf), it seems that using cplexAPI to solve quadratic programs or linear programs with a quadratic constraint is much more difficult. I tried to look over the package documentation, but I have no clue on how to do so.
Therefore, may I know how to use cplexAPI to solve quadratic programs or linear programs, or if there is any code samples for these two tasks?
In addition, the package Rcplex seems to be pretty similar, but its last update is already more than 5 years ago. So it would be really nice to know how the above two tasks can be done using cplexAPI in R. Thanks!
with cplexAPI you may use addQConstrCPLEX to add quadratic constraints

Is there a way to plot the solutions, feasible region and the optimal solution for Linear Programming in Julia Language?

I'm wondering if ther is a package to plot the feasible region (based on the constraints) and the optimal solution for linear programming in Julia Language using Juno. Do you know a way to do this? Suppose we have a LP problem and want to visualize the region and optimal solution. Is there a package to do this? How can I do this. I would appreciate so much your help. Thanks.

Mathematical constrained optimization in R

I have a mathematical optimization which I wish to solve in R consider this system/problem:
How Can I solve this problem in R?
In this model Budget, p_l for all l and mu_target are fixed constants while muis a given m-dimensional vector and R is a given n by m matrix.
I have looked into constrOptim and lp but I don't have the imagination to implement the constraints
Those functions require that I have a "constraint" matrix but my problem is that I simply don't know how to design that constraint matrix. There are not many examples with decision variables on both sides of the equations.
Have a look on the nloptr package. It has quite extensive documentation with examples. Lots of algorithms to choose from, depending what problem you are trying to resolve.
NLoptr link

How to show all possible solutions with lp solve with r

My idea is to start using lp solve in order to solve a linear programming model. As a result, I studied the lp function and his components.
However, one thing which is not clear to me is how do I display all possible optimal solutions using lp solve in R without my variables be binary?
I would appreciate an easy example to better understand.
Thanks,
David

How to find several solutions of nonlinear equation using R e.g. nleqslv?

As far as I understand R's nonlinear equation solver nleqslv(x, fn) finds only one solution of the nonlinear equation.
However (as Bhas commented) searchZeros function (the same package) can find my solutions depending on the starting points.
Question: are there some function in R which can help choosing the set of initial points for searchZeros ,which will help me to find all the solutions ?
I am interested in the case of function with several variables.
I undestand that solution to be found pretty much depends on the initial approximation. So the brute force way is to check some reasonable grid of intial approximations. However there might be some more intelligent way to get all the solutions ?

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