# Questions tagged [mathematical-optimization]

Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.

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658 views

### PenaltyFunction Option in NMinimize

I am curious if anybody has some experience in using the built-in Option "PenaltyFunction" in any of the numerical optimization functions like NMinimize. According to the documentation the user ...
128 views

### Linear programming with lazy constraints

Does Mathematica offer any means for solving linear programming problems with "lazy constraints", as described e.g. here? While I am not very familiar with linear programming, my understanding of the ...
298 views

### Customized StepSize control in unconstrained gradient-descent optimization

I have a type of minimization problem I frequently solve that involves warping a large 2D triangle-mesh (~25,000 vertices) to fit a model. In the mesh, vertices carry the empirical measurements (each ...
131 views

### LinearProgramming returns an invalid null solution that apparently doesn't satisfy constraints without any warning

Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later While searching to answer the question Solving the magic backyard puzzle with MMA at some time I composed a set of arguments ...
3k views

### Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
112 views

### StableMarriage vs. FindIndependendEdgeSet: How to use the procedure FindIndependendEdgeSet as a Gale-Shapley algorithm?

From Help, the procedure StableMarriage was an element of the Combinatorica, but it is available in the built-in ...
163 views

### FindShortestTour causes kernel crash

I have contacted support, CASE:4075709 UPDATE I have received reply from wolfram support. They have confirmed that this is indeed a bug. There are lots of sets of data that can cause the Kernel to ...
365 views

### How to determine reason for kernel crash? -> Nelder Mead optimisation

I am making use of the Nelder Mead algorithm inside Mathematica's NMaximize to find a parameter set by solving the Schrodinger equation for a given system. (see ...
789 views

### Visualizing the Lagrange Multiplier Solution

This question is based on work in Susan Colley's Vector Calculus, 4th ed. The question is to find and classify critical points of $f(x,y,z)=3xy-4yz+5xz$ subject to the constraint $g(x,y,z)=3x+y+2z=13$...
2k views

### When using NMinimize[…,Method->“DifferentialEvolution”] is an “iteration” different than a “step”?

Hopefully this question has a simple answer. I have the following bit of code: ...
77 views

### Caveats of LinearProgramming on Integers domain

When using LinearProgramming with the Integers domain, Mathematica issues the following warning: ...
111 views

### Optimize a network topology?

I'd like to know if one can use optimization function like Maximize[] or BayesianMaximize[] to optimize the hyper-parameters of ...
318 views

### Is there an analogue of Evaluated->False (in FindRoot) for FindMinimum?

I guess functions like FindRoot, FindMinimum, etc puts the estimation number into the expression, and then do other calculations....
404 views

### Custom Methods for NMinimize/NonLinearModelFit

Is there a way to write custom methods for NonLinearModelFit or NMinimize? To give background, I currently have a batch of code ...
384 views

### Problems extending NelderMeadMinimize into 2D

Update The eventual route I followed was to adapt a version of the NM-simplex written in C and link to it with MathLink. Once I've tested this out fully I'll post it here. I've been playing around ...
201 views

### Issue with FindCurvePath

I have a problem with the function FindCurvePath. In some cases it crashes the Mathematica 9 Kernel. Here an example, where it crashes the kernel: ...
122 views

### What's BayesianMinimization and related functions based on?

Is it specified anywhere what the backend is for the Bayesian optimization related functionality in Mathematica v11? I'm specifically referring to the Bayesian* ...
357 views

### Amelioration of a Karush-Kuhn-Tucker nice code

In what concerns the resolution of a Karush-Kuhn-Tucker condition, this wonderful code borrowed to Parreiras (The Mathematica Journal 16 2014) which is a correction of another code by Kampas (The ...
302 views

### Softmax Regression Classification Algorithm

I'm following the Stanford Machine Learning course while simultaneously developing my Mathematica abilities. I'm having issues with my Softmax Classifier implementation (for ref, have a look at these ...
272 views

### NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
256 views

### Problem with the accuracy of the real-coded Genetic algorithm

Since there is no Genetic algorithm implemented in the Mathematica i tried to write a very simple genetic algorithm myself. The accuracy of the results depend upon rounding up the obtained parameters. ...
874 views

### How to find the a minimum cost perfect matching

Crossposted on Wolfram Community A a minimum cost perfect matching is very useful tool.This three links about this demand just related me,let alone all MMA.SE. How to get some pairing with smallest ...
89 views

### How to do parallel computation when using LinearProgramming function?

I have a LP problem which contains 2n+3 variables with 4n+6 inequality constraints. I was trying to use Mathematica's LinearProgramming function. When n is small, like less than 30, it gives outcome ...
66 views

### OptimizationFindFitObjectiveFunction and PenaltyFunction

Consider the following toy example: model = a Cos[w t]; data = Table[{t, Cos[2.1 t]}, {t, 0, 10, .25}] + RandomReal[.1, 41]; as both an unconstrained problem: <...
199 views

### Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
193 views

### NMinValue , NMaxValue , NMinimize and NMaximize behave poorly for 2-dimensional function unless the constraint is posed as an ImplicitRegion

I am making a plotting function where I need to know the max value the function takes over the given 2D range. I noticed a difference between the behavior of ...
148 views

### Improving the speed of an optimization algorithm via compilation and parallellization

I have written an implementation of eight variants of the PSO-algorithm and I want to test them over a set of test functions. I am using parallelization as it improves the speed a lot and I have also, ...
213 views

### Symbolically Minimizing a Max function

I'm having a tough time with seemingly simple symbolic Minimization/Maximization in Mathematica. I would like to use the Maximize function to work on some unknown random variables and so use min/max ...
124 views

### Efficient processing of Special Ordered Sets with LinearProgramming

I'm playing with integer linear programming, especially problems involving lots of constraints which would appear to be special ordered sets. Below is a toy example, three last rows of the matrix ...
563 views

### Travel time sweet spot using: Mathematica and Google Maps API

I want to use Mathematica to do some time minimisation calculations calling on Google Maps API for travel time data. I'm concerned with travel time, e.g. along roads (by car or walk) and not linear ...
61 views

### Mathematica implementations of classical genetic algorithm optimization

Are there any Mathematica implementations of genetic algorithm optimization routines, including third-party and commercial? (DifferentialEvolution isn't quite what ...
59 views

### Plotting gradient and newton directions for parametric system of nonlinear ODEs

I have a bucket (system) of chemical kinetics models, a nonlinear dynamical system given by: where kf >= 0 and kr >= 0 are the parameters. The initial conditions are A(0) = B(0) = 1 and C(0) = 0. I'...
164 views

### Speeding up an optimization problem

I have the following code which is working well but for matrices $M_i$ of size $40000\times 4$ the optimization problem takes extremely long. ...
56 views

### NMaximize not finding initial points within simple constraints

I'm trying to do an optimization, but Mathematica seems not to be able to find starting coordinates within a simple rectangular region. When I run this code: ...
214 views

### Automated searching for maximal 2D point configurations

I have some black-box function that takes lists of 2D points, and I would like to find some practical methods of searching for collections of points that maximize it. Motivation I've come across ...
94 views

### Finding the shortest distance of two points and an area

So I have a region defined by something like MeshRegion[{{0, 0}, {1, 1}, {2, 1/2}, {2, -1/2}}, {Line[{1, 2}], Line[{2, 3}], Line[{3, 4}], Line[{4, 1}]}], and two ...
110 views

### Combinatorial Optimization of NFL Games

This is a "fun" optimization problem that was prompted by an NFL betting pool. Each week you pick one team to win. If that team wins you stay in the game. If it loses you're out. The catch is that ...
66 views

### Use Principal Axis Optimizer for constrained Problem

The "Principal Axis" Optimizer described here works particuarly well on my problem. Now I do know some constraints about my problem and would like to implement them to make it faster. Even though it ...
62 views

### “ParallelDo” does not calculate the function well

Now, I'm solving utility maximization problem. ...
107 views

The command ...
188 views

### Issues with methods of FindMinimum

I'm trying to use the function FindMinimum for portfolio optimization in stead of NMinimize, since the latter is a lot slower. Also because the variance function of my portfolio is convex, locally ...
121 views

### Possible memory leak in FindMinimum? (MMA v10.0)

So I was running some code when I noticed Mathematica was gulping memory, and after some debugging I think the culprit is found. It turned out the function ...
356 views

### Using NMaximize to get integer results for a fractional programming problem

I have an optimization problem that I am trying to model in mathematica (wolfram cloud, to be precise). Link to notebook for code described here: https://www.dropbox.com/s/4jet4t76fe5pysk/...
80 views

### Where can I find detailed information about the SystemOptions?

I'm looking to optimize my Mathematica script, and I'm willing to go spelunking with low-level system options. The problem is that I've been looking in the Mathematica documentation, but there doesn'...
859 views

### Speeding up NDSolve for system of differential equations

I am wondering if there is a way to speed up this function that solves a system of ordinary differential equations with NDSolve? Thus far I've tried specifying a few different methods such as LSODA, ...
322 views

### Optimization with Matrix value constraint

I am trying to find the orientation and position of a polygon resting on a curved surface under gravity.The polygon MUST not be penetrated by any part of the surface below. Here is an example for a ...
229 views

### Trouble with Minimize

Minimize[{t^2, 1 == 3*t + 16*u}, {t, u}, Integers] It does not give the solution t = -5 and u = 1. Am I missing something? The solution being known and ...
462 views

### Speeding up a numerical constrained quadratic optimization

I'm trying to solve a quadratic optimization problem in 35 variables, $\vec{α} = \left< α_1, \ldots, α_{35}\right>$:  \begin{aligned} &\operatorname*{maximize}_\vec{α}&&1.0\cdot ...