# Tag Info

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### Is there a constrained nonlinear optimization library like IPOPT that runs on GPUs?

tl;dr: My general impression from the literature is that speedups are modest (if they exist). The main kernel you'll see in these methods is a sparse-direct method (e.g., sparse LU, sparse LDLT), and ...
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### Is there a high quality nonlinear programming solver for Python?

We recently released (2018) the GEKKO Python package for nonlinear programming with solvers such as IPOPT, APOPT, BPOPT, MINOS, and SNOPT with active set and interior point methods. One of the issues ...
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### Piecewise linear optimization with resource allocation constraints

If $P_i(w)$ is a piecewise linear, convex function, then it can be written as the maximum of a number of linear functions, $P_i(w)=\max \{L_{i1}(w),\ldots,L_{iJ_i}(w)\}$. Then, the optimization ...
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### Example Problem to Demonstrate BiCGStab

Check out Matrix Market. It has a nice collection of matrices from different areas (fluid dynamics, elasticity, acoustics etc.) So you do not need to assemble systems yourself in order to provide ...
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### Constraints 'exactly/at most one non-zero element' without binary variables

No, this is not possible. There is a standard way of showing this: The feasible region of your constraints is not convex. For example, $x_{1,1}=1$, $x_{1,2}=0$ is feasible, $x_{1,1}=0$, $x_{1,2}=1$ ...
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### How to solve the following Frobenius norm-minimization problem?

\big\| \mathrm A \begin{bmatrix} \mathrm X & \mathrm X^2\end{bmatrix} - \begin{bmatrix} \mathrm B_1 & \mathrm B_2\end{bmatrix} \big\|_{\text{F}}^2 = \underbrace{\| \mathrm A \mathrm X - \...

### MINLP with GEKKO - Modeling discrete variables

If they don't have a variable that is constrained to a discrete set you can formulate it like so: ...
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### MINLP with GEKKO - Modeling discrete variables

Below is an example of using Gekko (v0.2.4+) to define a SOS1 variable with an objective function to find the minimum in that sequence of values. ...
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### GAMS solvers: which one to use

Somewhere in the GAMS file, after you've declared almost all of your model, you have to write a solve statement of the form ...
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### Find $\min \sum_{1\le i\le n} x_i\mathbf{z}^T\mathbf{A}\mathbf{y}_i +\mathbf{b}^T\mathbf{x} +\cdots$

I'm looking forward to your comments to the following solution. We will solve the problem for the constraints $\mathbf{1}^T\mathbf{x}=\mathbf{1}^T\mathbf{y}_i=\mathbf{1}^T\mathbf{x}=1$ and for a ...
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### Is there a high quality nonlinear programming solver for Python?

How about calling Matlab from Python, using python-matlab-bridge or the like ? That looks much easier than porting yards of code, not to mention test cases and doc. And general: any Python $\to$ any ...
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### Large-scale nonlinear optimization problem

At 1 million variables, you're sort of on the cusp of what a code like (the publicly released version of) IPOPT can do. IPOPT will solve the KKT system derived from an interior point method using ...
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### A separable nonnegative quadratic program

With $d=16$, the $Q$ matrix is just 256 by 256. Thus the individual subproblems are quite small. Your $Q$ matrices are singular, so the optimal solution to each of the subproblems is likely to be ...
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### Optimization with matrix determinant as constraint

The constraint $\det(A) > 0$ is very unstable and absolutely horrible. Would you believe that on practical, non-contrived 6 by 6 symmetric matrices, changing one element of the matrix by 1e-15 can ...
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### Symmetric nonnegative matrix factorization

I'm going through some of my old StackExchange posts and came across this one. As it turns out, the answer led to a section in a published paper! As detailed in that paper (and in its notation), if ...
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### Is there a constrained nonlinear optimization library like IPOPT that runs on GPUs?

I'm a little late to the party, but the short answer is that yes it's possible to parallelize an interior point method for GPUs, but whether or not that is successful depends on the structure of the ...
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For the discrete version, it can be cast as a mixed-integer linear program. You just have to note that every element $x_i$ can be written as $x_i = \sum_{j=1}^k \frac{\delta_{ij}}{j}$ where \$\sum_{j=1}...