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

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10
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271 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 ...
9
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0answers
95 views

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

Bug introduced in 10.3.1 or earlier and persisting through 10.4.1 While searching to answer the question Solving the magic backyard puzzle with MMA at some time I composed a set of arguments ...
6
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0answers
87 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 ...
6
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0answers
237 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 ...
6
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0answers
289 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 ...
6
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0answers
170 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: ...
5
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0answers
204 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 ...
5
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0answers
148 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 ...
5
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0answers
152 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 ...
5
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656 views

Semidefinite Programming

I want to solve a numerical optimization problem using semi-definite programming. Is there a package or add-on that equips mathematica with this functionality?
4
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57 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 ...
4
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0answers
356 views

Precision and accuracy in NDSolve and NMinimize

I use NDSolve quite a lot and have noticed that setting values for AccuracyGoal and ...
4
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265 views

Packages for Semidefinite programming

This question has already been asked here. I am not sure, whether I should have asked this question as a comment of an old question or in the general programming forum of stackexchange. Moderators ...
4
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819 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: ...
3
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0answers
92 views

Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
3
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0answers
70 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 ...
3
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0answers
78 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, ...
3
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0answers
81 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: ...
3
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0answers
85 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 ...
3
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0answers
95 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 ...
3
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0answers
372 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 ...
3
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0answers
254 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 ...
3
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0answers
194 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 ...
2
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0answers
65 views

Complicated implicit plotting - can it be tackled?

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
2
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0answers
30 views

EvaluationMonitor vs. StepMonitor in Simulated Annealing

I am trying to track the evolution of NMinimize using the SimulatedAnnealing options. Simulated annealing has 3 parameters to track: 1) the latest trial point, 2) the latest accepted point, 3) the ...
2
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0answers
78 views

Findminimum fails in loops

Introduction to the problem: the function F[x][u,v,w] I'm currently dealing with a very strange minimalization problem. I have a function F[x][u,v,w] which is ...
2
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0answers
129 views

Linear Programming Using Dual Simplex method

I want to solve an optimization problem using the Dual Simplex Method. Although Mathematica gives the result directly when I use the command Minimize but I want to ...
2
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0answers
67 views

FindMinimum pre-conditioning

I am wondering about what kind of pre-conditioning FindMinimum performs on the user specified function (to be minimized) before the actual minimization starts, and ...
2
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103 views

Appropriate method for a Non-linear Optimisation Problem, With Linear Constraints,

I have a small non-linear, chess related, program with linear constraints and an objective function obtained from a polynomial probability generating function including some decision variables . At ...
2
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0answers
49 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 ...
2
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0answers
264 views

Maximizing Large Multivariable Function over Region with Parameter Constraints

Brand new Mathematica user here. I have a complicated function to maximize, and thought I would try software like Mathematica instead of taking derivatives by hand. I found some Mathematica ...
2
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0answers
141 views

Combination of linear programming with bilevel optimization

I'm not a programmer really (interested in mathematics actually). Excuse me if I can not coding good. I'm also interested in implementation of mathematics results in programming language. That's my ...
2
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0answers
315 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 ...
2
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0answers
329 views

Why my Mathematica 9.0.1 wont work with some samples of Mathematica in Graph Theory?

Bug introduced in 9.0 and fixed in 10.0 FindMinimumCostFlow is introduced in 9.0. I updated my Mathematica recently to 9.0.1 cause the previous version was ...
2
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0answers
511 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
2
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0answers
303 views

Having difficulty with the Minimize command

I am having trouble getting an answer to this question...Am I missing something that anybody can see. ...
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0answers
44 views

Can Mathematica solve Kuhn-Tucker Equations with arbitrary functional form (up to 2nd order derivative)

I am in a business of solving a 5-variables optimization with inequality constraints, and I would like to maintain the functional form as arbitrary as possible. So far, I am assuming that the ...
1
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0answers
57 views

NMinimize / adding constraints

I have a quick question: in question:Solving an ODE with boundary conditions at infinity and 0//different problems, I asked for help concerning a differential equation- however, the whole solving ...
1
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0answers
77 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 ...
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0answers
45 views
1
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62 views

Exponential Matrix Diffentiation

I have been struggling with the following question while solving an optimization problem in $\mathbb{R}_{+}^G$. Basically, I have $$\min_{y \in \mathbb{R}_{+}^G} F(y) = y^{T}\mathcal{K} + \exp(-y^{T} ...
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0answers
52 views

Trying to minimize a function over the integers

I am trying to evaluate the following expression. ...
1
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0answers
59 views

Find multiple optimization parameters of Max-Min problem in numerically

I have an optimization problem $$\max \min [x_1,~\cdots,~x_m,~\cdots,~x_M]:~M\geq 2$$ where $$x_m=P_m(1-a_m)\prod_{j=1}^{m-1}\left(\frac{a_j}{1-a_j}+b_j\right)$$ and $$0\leq a_i<1;~~0\leq ...
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0answers
45 views

Evaluation of likelihood very slow

I am trying to implement a simple statistical model for the first time in Mathematica. My model is made my one random variable which is the sum of background and signal. Background is an exponential ...
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0answers
88 views

Method used by NMaximize with a binary linear problem

I'm using Mathematica 7's NMaximize to solve a linear programming problem with thousands of 0/1 integer variables, thousands of linear constraints and a linear target. I suppose I could use ...
1
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0answers
110 views

Maximize and NMaximize don't work for my function

I defined the following function: d1[x_] := Min[Abs[FractionalPart[x]], 1 - Abs[FractionalPart[x]]] and tried to evaluate the following function: ...
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0answers
134 views

How can I speed up this NM optimization? Most delay seems to be due to long analytic expression

I am struggling with computational speed of a NelderMead optimization. Nevertheless my impression is that I lose lots of speed not only due to the NM optimization itself but rather to for instance ...
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0answers
168 views

Imposing constraints to NMinimize/NMaximize leads to wrong function values

I wrote a function that uses NMaximize to find certain parameters (using NelderMead simplex algorithm). My objective functional $J({x_i})$ is real-valued and its ...
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0answers
187 views

How to plot feasible objective space of a Generic Multiobjective Optimization problem?

As you know, a generic Multiobjective optimization problem can be stated as follows: $min{\space}F(\bf{X})=[f_1(x),...,f_n(x)]$ $h_k(x)=0{\space\space\space} k=1,...,n_e$ ...
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0answers
176 views

Nash equilibrium in game theory?

Are there examples of the solution of Nash non-cooperative games with mixed or pure strategies? How could be implemented in Mathematica 10?