9 votes

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 ...
John Hedengren's user avatar
5 votes

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 ...
wyer33's user avatar
  • 757
5 votes
Accepted

Gradient of function after renormalization of variables

Based on your current optimization strategy, it is likely you cannot get away with just the gradient of $f(\cdot)$ evaluated at $\frac{\boldsymbol{x}}{\left| \boldsymbol{x}\right|}$ since ...
spektr's user avatar
  • 4,228
5 votes

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: ...
Richard's user avatar
  • 3,961
4 votes
Accepted

Optimisation of purely integer quantity with bound-constraints for a 1D expensive function whose analytical form is not available

@Stellos already gave the correct answer, but let me try to back it up with a bit of intuition: Think of your function $f(x)$ as a function that would actually make sense for any real-valued argument ...
Wolfgang Bangerth's user avatar
4 votes

How to solve a constrained optimization problem using minFunc or minConf

Adding another answer, as I just realized that the problem is easily solved as a linear SDP. Let $Q=S^TS$ and you have the objective $\mathrm{trace}~Q + \mathrm{trace}~Q^{-2}$. Introduce an upper ...
Johan Löfberg's user avatar
4 votes

How to solve a constrained optimization problem using minFunc or minConf

Not a direct answer to your title question, but I think you are better off attacking this problem from the semidefinite domain instead. Trivial approach is to linearize the objective at some initial ...
Johan Löfberg's user avatar
4 votes
Accepted

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 ...
56th's user avatar
  • 901
4 votes
Accepted

Largest hypercuboid inside a polyhedron

It turns out that the problem has quite an elegant solution. Let the hypercuboid be defined by $\mathbf{l} \leq \mathbf{x} \leq \mathbf{u}$ instead of using the more cumbersome $\mathbf{x_{0}}$ and $\...
gpavanb's user avatar
  • 572
4 votes
Accepted

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, $x_{1,1}=0$, $x_{1,2}=1$ ...
Brian Borchers's user avatar
4 votes
Accepted

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. ...
John Hedengren's user avatar
3 votes
Accepted

Why can't we discretize continuous domains in distributed non-convex constraint optimization problems?

You are missing that, in general, integer optimization problems are much more expensive to solve than real-valued optimization problems. That's because for real-values optimization problems, you have ...
Wolfgang Bangerth's user avatar
3 votes
Accepted

SOCP: Recovering primal from dual

The standard technique is to solve the optimality conditions as a linear system of equations. Let us rewrite your problem into standard form $$ \begin{align*} \text{maximize } & -c^{T}x\text{ s.t. ...
Richard Zhang's user avatar
3 votes
Accepted

Minimizing linear objective on intersection of convex sets

See this recent paper on an extension of stochastic gradient descent that could be used on your problem: https://arxiv.org/abs/1511.03760 You could also apply Dykstra's algorithm (or any other ...
Brian Borchers's user avatar
3 votes

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

Generally nonlinear optimization is hard to parallelize because its stepping algorithm is very sequential. GPUs are slower than CPUs so you only get a speedup if you have your problem as something ...
Chris Rackauckas's user avatar
3 votes
Accepted

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 ...
Justin Solomon's user avatar
3 votes
Accepted

Piecewise-Linear Quadratic Optimization for an "Almost Convex" Problem

You could implement the piecewise linear functions using SOS2 variables (SOS2=Special Ordered Sets of Type 2). This approach does not care about convexity (that is, convexity related to the piecewise ...
Erwin Kalvelagen's user avatar
3 votes

Geometric Programming - symbolic version

You may want to give SCAT Maple package a try. It is certainly not tailored to geometric programming but is worth trying. C. Hamilton "Symbolic Convex Analysis" thesis from 2005 describes the ...
Anton Menshov's user avatar
  • 8,652
3 votes
Accepted

Setting up optimization problem in GEKKO

A good first step with any parameter estimation problem is to solve it in simulation to verify that you can get a good solution and that the parameters have an effect on the objective. You can first ...
John Hedengren's user avatar
3 votes

What's the right choice of variable settings for setting up my optimal control problem?

The m.MV() type has additional tuning parameters such as move suppression that is likely contributing to the difference in solution. Also, the ...
John Hedengren's user avatar
3 votes

A question related with $p$-Laplacian and conjugate gradient method

You seem to be misunderstanding the difference between the derivative of $E$ and the gradient of $E$. I am going to assume that $u$ lies in an appropriate Sobolev space $V$, which embeds continuously ...
whpowell96's user avatar
  • 2,259
3 votes

optimizing piecewise linear objective functions (perhaps non convex) with equality constraints

For global optimization of black box functions, I have successfully used scipy's differential evolution (https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html)...
Victor Ruela's user avatar
2 votes

Is there a high quality nonlinear programming solver for Python?

KNITRO has Python and MATLAB interfaces, among others. Think of it as an FMINCON replacement, but much better performing, and more expensive. https://www.artelys.com/en/optimization-tools/knitro#doc-...
Mark L. Stone's user avatar
2 votes

Is there a high quality nonlinear programming solver for Python?

How about CMA-ES? It has Python bindings and is well suited to nonconvex, nonlinear optimization problems and I've used it quite a bit: https://www.lri.fr/~hansen/cmaesintro.html Installation through ...
Brian's user avatar
  • 121
2 votes
Accepted

How to efficently solve: min $\sum_{ij}(a_{ij}x_{ij}^2 + b_{ij}x_{ij})$ s.t

This is a regular positive definite quadratic minimization problem with linear constraints. It should be trivial to solve using one the usual methods for this approach. A simple approach would be, for ...
Wolfgang Bangerth's user avatar
2 votes

Optimisation of purely integer quantity with bound-constraints for a 1D expensive function whose analytical form is not available

Without any information/insights about $f(\cdot)$, your only option to find the maximum is by brute force, i.e., evaluate $f$ for all integers. Now, if this is is practically impossible to do, your ...
Stelios's user avatar
  • 731
2 votes
Accepted

Obtaining a feasible solution for underdetermined system of linear equations satisfying inequality constraints

The problem was already solved in the comments section using linprog. Also CVX... I wanted just to point out that fmincon can also be used: just set the linear ...
Beni Bogosel's user avatar
  • 1,025
2 votes

Perturbation in bounds given the perturbation to constraints

I assume that you're interested in $b-\epsilon \leq a^{T}x \leq b +\epsilon$ rather than $b+\epsilon \leq a^{T}x \leq b +\epsilon$ right? If you're interested in more complicated ...
Brian Borchers's user avatar

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