Questions tagged [mathematical-optimization]
Questions on the optimization functions of Mathematica such as FindMinimum/FindMaximum, Minimize/Maximize, NMinimize/NMaximize, etc.
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Express polynomials as sum of squares
Well, while SOStools of Matlab can express a polynomials as SOS (Sum Of Squares) by the following theorem:
A multivariate polynomial p in n variables and of degree 2d is a sum of squares if
and only ...
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Optimization problem with parameter dependent interval of functions
I am working on an optimization problem but ran into a problem.
Here is a simplified version of the problem:
...
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Choice of initial values for FindMinimum
I have been using the FindMinimum function in Mathematica to implement nonlinear regression (for function $f(x,y)$, say).
I am curious to find how the starting ...
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Solution to a linear equation with minimum rank
Suppose I have a linear equation, $X.M=A$, for given matrices $M$ and $A$. I can use FindInstance to produce a solution $X$.
How can I add the constraint that $X$ has the least rank?
Indeed, I could ...
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RegionPlot of the Maximum of a function
For the function fun[a_, b_, x_, y_] = Sin[a x] Cos[b y] (a x + b y);corresponding to $x$ and $y$, I need a RegionPlot showing the maximum of function $fun[a, b, x, ...
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A problem of nonlinear multi-objective optimization
I have two variables x1 and x2 and I use them to calculate 4 metrics y1,y2,y3, and y4. now I want to solve for the value of x1 and x2 so that these four metrics are as large as possible. Can anyone ...
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Using Compile on Gradient within FindMinimum efficiently
This is an example from the documentation:
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Expressing a polynomial as a sum of squares
I encountered a degree 4 polynomial in 8 variables f(a1,a2,a3,a4,b1,b2,b3,b4) that I suspect can be written as a sum of squares. While sostools in MATLAB would find ...
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Real valued solution
I want to obtain the critical points or if you like a real solution for the first derivative of the function set to zero, and the second derivative also vanishes of the function :
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Nonnegative Least Squares Algorithm (NNLS) [closed]
Can anyone optimize the code below which is developed in an old version of Mathematica (2003) both in terms of efficiency and adaption to the latest versions of Mathematica?
Description of the code:
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Approximate strictly positive solution to a linear set of equations?
Consider a positive matrix M and a positive vector b, e.g.
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Minimum of a function that depends on several variables
I have a function,
$$A=\sum_{m}mx$$
provided
$$x=\frac{2(y1+iz)}{2t1-\left|\frac{t2}{iy2}+z\right|}$$
Here $$y1,z,t1,t2,y2$$ all are varying. But $x$ needs to be in the limit of $-1$ and $0$. Is there ...
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Find min value of a complex Root function [closed]
Could someone tell me how to obtain the min value of this function when lambda is between 0 and 1:
...
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Optimize cost when ordering wood boards (cutting stock problem)
That is probably a common optimization problem, but I don't know how to solve it efficiently.
Say you want to buy the following wood boards: 2 to 1m, 3 of 1.5m, 2 of 2m. The shop has the following ...
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Specify a constraint on an interval under FindMinimum
I have an interpolated function that looks like this:
$\hskip1.2in$
and, based on extreme and critical points, I want to use a polynomial to approximate the function. The points in question are:
<...
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Find the maximum of a given function
I calculate a target function f about two variates a and b.
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How to take the derivative with respect to a function with more than one variable?
I have a function that includes another function inside. I want to know the derivative at every point x. I have spent a lot of time trying to figure out how to do this, but I am very lost. I have ...
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Solve overdetermined set using Mathematica?
As shown below, this is a overdetermined system. Could you teach me how to find the optimized solution in Mathematica? I know it could be solved by the method of least square, but how to realize it in ...
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Solving a system of equations as part of maximizing a multivariable function
This is my code
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How to optimize the $L^{2}$ norm in Mathematica for an iteration scheme and How to plot its 3D graph?
Consider the BVP $y^{\prime\prime}(t)=\frac{3}{2}y(t)^{2}$ with boundary conditions $y(0)=4$ and $y(1)=1$. The initial iterate is in this case $x_{0}=4-3t$. The higher iterates are given by the ...
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How to get a rational solution of the linear system efficiently?
I got a large linear system
...
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Finding element selected in NMaximize[{Min[...], constraints},{vars}]
How can I determine which element of Min[] is being selected in a NMaximize[{Min[...], constraints},{vars}] problem? For example,...
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NMinimize and DE
I would like to use the Differential Evolution option of NMinimize to find the "optimal" solution for the hyper-sphere function defined as follows,
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Is is possible to specify use of a non-Euclidean norm for NonlinearModelFit
When using NonlinearModelFit with Method->NMinimize I have received the warning message NonlinearModelFit::lmnl, which includes the text
""The model -cVar+Log[1+0.00821596 t] is linear in ...
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Boolean constraint in an interval for FindMinimum
I have a function with a large number of variables that I am trying to minimize subject to some constraints, but for simplicity let us say that it only has two variables, f[x, y]. The constraint is ...
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My model has not finished evaluating in more than a day so can't test if it works, what is wrong with it?
Hello I have this modified monocentric city model that I have been working on for a while.
Sorry for the long post, I wanted to add the whole code, because it's all connected.
My suspicion is that it ...
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Local extrema points of a function of two variables
i need to find local extrema points of a function of two variables, but it doesnt work
FindMaximum[x^3 - 2 y^3 - 3 x + 6 y, {x, y}]
I have this error:
...
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2
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Minimax / Minmax optimization
For the complex polynomial $$P_n(z) := 1+z+\frac{z^2}{2} + \sum_{j=3}^n \gamma_j z^j,\quad z \in \mathbb C.$$ I want to solve the following minimax/minmax optimization problem:
$$\min_{\gamma_j} \max_{...
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How can I quickly find the coordinates of key points? [closed]
There are 1000 points in the space. The coordinates are (0,0,0) - (9,9,9). Any point can cover all points on the three straight lines (parallel to the X, Y and Z axes respectively) where this point is ...
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Finding local minimum of a 2D potential
I tried to find a local minimum point of a 2D potential U[\[Chi],\[CurlyPhi]] with both FindMinimum and ...
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Norm adding up residual
For FindFit I want to have a norm that just sums up all residuals.
For the sum of absolute values there is NormFunction -> (Norm[#, 1] &), but I don't know ...
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Implementing an optimization algorithm in WL
I am trying to implement the Jaya optimization algorithm (Jaya). This is a flowchart from the Author 's webpage showing the details of the Algorithm.
Note that there is a typo in the equation in the ...
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Issues with ConvexOptimization and SetPrecision
I am completely new to Mathematica (second day), so do not expect things to look polished.
I am trying to perform a ConvexOptimization over a List/Array (dimensionality ...
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Is there a faster way to solve this linear programming problem?
I need to get a rational solution of the linear constraints
...
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Parametric minimization of a quadratic expression in two variables
I am not an expert in using Mathematica, and I do not understand the following result (apologies if it appears trivial). I want to find the general solution to minimize the following expression over $...
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How to provide an RNN various type of inputs?
I'm trying to build an RNN in Mathematica.
My window is only 2 but the variables are of different types:
...
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Steiner Trees for Unit Polygons?
I know this is a longshot, and it's a rather broad question, but hopefully someone can help. Is there a simple or fast way to find Steiner Trees for unit polygons using Mathematica? By unit polygon, I ...
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Two problems with ConjugateGradient
I am trying to solve a maximization problem for which I give you the code and try to step by step show you were it broke down. The first issue is that I have a constrained problem, which I try to ...
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When can you guarantee Minimize outputs the global minimum? [closed]
In the Minimize documentation, it's stated that "Minimize will return exact results if given exact input. With approximate input, it automatically calls NMinimize."
What is an approximate ...
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NMinimize does not reach the minimum
I need to minimize numerically an expression with constraints. The expression also includes a numerical integral (called 'PNoninteract').
The minimization apparently stops prematurely (I know roughly ...
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Find the maximum value of the minimum eigenvalue of the matrix
There is a $4×4$ matrix $Q$ where $c,d,e,m,n$ are variables.
How to get the maximum value of the minimum eigenvalue of $Q$?
$Q=$ $$\\\left(
\begin{array}{cccc}
\frac{12058305}{23104}-304 c & -849 ...
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Convex optimization of a least squares regularized objective function [closed]
Given, a vector of observations $\mathbf{y}=(y_1, y_2,\ldots,y_n)$ I am trying to find the soltuion to the following optimization problem:
$$
\min{ (1/2) \|\mathbf{y-x}\|_2^2 + \lambda \|\mathbf{Dx}\|...
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How to numerically solve an equation
I would like to solve for $r_2$ the following two (independent) equations:
$x_{Min}(a,b,c,r_1,F)=x_{Max}(a,b,c,r_2,F)$ (1)
and
$x_{Min}(a,b,c,r_2,F)=x_{Max}(a,b,c,r_1,F)$ (2)
where $a$, $b$, $c$, $r_1$...
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Simplification of long trigonometric expression taking a long time
I have tried to Simplify as well as FullSimplify a long trigonometric expression to get a simplified form of the expression but it takes a very long time almost hours and sometimes it also shows error ...
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Selecting a set of points from a region to maximize the smallest pairwise distance
Suppose, we have a region (say, for simplicity, a unit cube) and a distance function that, given the coordinates of any two points in the region, calculates the distance between them. It is not simply ...
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Plot issue : put a legend instead of a top label
I have an issue about putting a legend consisted of a text and numerical value instead of a label.
For example, with this command line :
...
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Plot issue : bad label ordering with concatenation of strings
I have an issue about a label which is consisted of a variable name [Omega]BD and a numerical value associated.
Firstly, I put the BD subscript to ...
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Minimizing a function over a bounded domain with binary variables
I want to minimize the following function:
$$
f(m,n)= \sum_{i=1}^N\Big\{ \alpha_i(x_i-m)^T(x_i-m) \Big\} + \sum_{i=1}^N\Big\{\beta_i (x_i-n)^T(x_i-n) \Big\}
$$
where $m,n$ are all 2-d vectors:
$$
m:= ...
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