# Questions tagged [optimization]

This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.

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### In a dynamical system, what might be a good reason why periodicity in an object's velocities is important?

I'm studying periodic motions in a dynamical system and, as a newbie, I narrowly think of an object's periodicity in its spatial x-y coordinates, but what might be a good reason why the existence of ...
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### Reference for learning the linear algebra of optimization [closed]

What's a good linear algebra reference for optimization that uses standard linear algebra curriculum topics such as inner products, orthogonality, gram-schmidt? Some of the current material I'm ...
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### Could not get expected result?

I am trying to solve the example 3.3 in this book. ...
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### Need Help for Formulating in YALMIP

I want to implement the given optimization algorithm for the ieee-14 bus system into YALMIP. It is a non-convex type of problem. it will be appreciated if anyone can help me in formulating this into ...
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### Interpreting multivariable root-finding results from Matlab's fsolve algorithm

Edit: So I was able to get the same value of r that's given, when coding up the sum of squares of function values directly in the script file, rather than on the Command Window. So, maybe there's a ...
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### Optimization for sampling multiple points of maximized minimum distance

I'm trying to find a way to sample new points that have maximum minimum-distance (maximin distance). The current situation is where there are ns number of pre-existing sample points. I want N number ...
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### Genetic algorithm: fitness proportionate selection using RMSD as fitness function?

I'm implementing a genetic algorithm to optimise $x$ so as to minimise the RMSD error $r(x)$ between my model and experimental data. During the selection stage of recombination, I wish to select '...
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### Making Hessian positive semidefinite

I have a large problem that I'm optimizing with Newton method. This involves a large sparse Hessian matrix. For better convergence and not to get stuck prematurely, I'd like to make the Hessian ...
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### Machine Learning for Optimization

I have a function which takes 100+ coefficients and outputs $x$. I wish to optimise $x$. Running the simulation 50 000 times will take around 15 minutes, however, this happens in parallel - and the ...
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### How to define a dimensionless Objective function for determining how peaked a curve is?

I have attached 2 plots for FFT spectra. One is considered good and one is bad. The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...
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### How do I get scipy.minimize to terminate below a certain loss threshold?

I was looking at the scipy.minimize documentation to see if I could find a way to terminate optimization when the loss gets below some cut-off, and I couldn't see ...
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### A concave maximization that is not supported on CVX

I try to solve a maximization problem using CVX. In its simplest form, I want to maximize $$f(x,y)=y*h_b\left(\frac{x}{y}\right),$$ where $h_b(\cdot)$ is the binary entropy function. In the context ...
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### Python: Getting second output variable from minimizing a computationally intensive function on first outputs

I have a function in python that is quite computationally expensive to evaluate, of the form: ...
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### Using MILP to place a set of primers along a genome

Define variables $p_i,u_i\in\{0,1\}^G$, for $i=1,\ldots,8$ and $G=30000$. Let $v$ be a constant vector also in $\{0,1\}^G$, with approximately 25% of its entries equal to $1$ (randomly located). Let ...
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### Plotting optimum as a function of parameter in the objective

I am trying to minimize a 2d function using scipy.optimize. Specifically I want to plot the minimum value of the function fun as a function of the parameter wjk. The problem is that I cannot pass wjk ...
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### How to minimize $(x-a)^2+(y-b)^2$ subject to $\sqrt{a}+\sqrt{b}=\sqrt{2}$?

I am not sure if this is on-topic here, but I am trying. Let $x,y$ be positive real numbers. I am trying to find $$\min_{\sqrt{a}+\sqrt{b}=\sqrt{2}}(x-a)^2+(y-b)^2$$ I tried using Mathematica for ...
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### Can Scipy.optimize take a user-defined objective function that contains an ML model?

I have an optimization task that requires me to choose the optimal combinations of parameters, according to the prediction of a random forest model. My main obstacle is that scipy.optimize always ...
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### Convex performance measure of classification

In the context of binary classifcation methods, I am looking for a performance metric that can be optimized in MATLAB. Since the data is not balanced, a good choice seems to be the so-called F1-...
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### Optimizing vectors with equal elements

I am trying to distribute power across different devices, so that the sum is as equal as possible to the power setpoint. At the same time, the sum of power per phase must not exceed the power of the ...
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### Avalability of SNOPT optimization solver

I'd like to know if SNOPT solver is available free of cost for academic research in any of the optimization software packages. I came across a few softwares that have SNOPT, but those require a ...
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### Does BFGS preserve the bandedness of the inverse hessian?

In the BFGS method we perform iterations by calculating an approximation $\boldsymbol{H}_k$ to the inverse Hessian $\boldsymbol{H}$ of the objective function. This method belongs to a family of ...
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### Detecting degenerate triangles with very thin structures

Between the two ears in the following bunny images, there are some degenerate triangles I want to detect. It looks like a volume-less thin slits. If the question is not clear, please let me know.
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### Inverse Newton Method for optimization: is this the correct algorithm?

I am trying to implement the algorithm in this article. I have already asked a question before about it here, and I am trying to figure out what I am doing wrong. This time, it's this section of the ...
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I want to estimated the parameters $\ \hat{\theta}$ of a model using an iterative search for the minimum of a cost function. The cost function is defined as follows: $$V_N(\hat{\theta}) = \frac{1}{... 1answer 121 views ### Which optimization method can be used to do the following? I've the following system of equations for studying information flow in the below graph,$$ \frac{d \phi}{dt} = -M^TDM\phi + \text{noise effects} \hspace{1cm} (1)$$Here, M is the incidence ... 2answers 99 views ### What online optimisation algorithm can be used for a noisy cost function? I am trying to optimise a function, but the function can be noisy and give varying results for the same parameters. Furthermore, it needs to be online, as the data from each new iteration happens ... 2answers 211 views ### log(det(X)) in Semidefinite Programming I have been solving problems of the form$$max \ log(det(A)) \\ s.t. \ A = A^{T} \succeq 0, \\ p_{i}^{T}Ap_{i} \leq b_{i}$$where b_{i} and p_{i} are input vectors (to be clear there is more than ... 1answer 96 views ### Arbitrary Precision Optimization Libraries? Are there any well-known optimization libraries (ideally with Python bindings or even in Python) supporting (unconstrained) minimization (of f:\mathbb{R}^n \to \mathbb{R} for n for n\sim 10^1,10^... 0answers 37 views ### exploding gradients in gradient descent procedure of multi-output ridge regression Multi-output ridge regression:$$W^{*}=\underset{W}{\arg \min } \frac{1}{\mathcal{N}}\|Y-WX\|_{F}^{2}+\lambda\|W\|_{F}^{2}$$There are Q outputs, N samples, and P covariates (features). \hat{... 1answer 72 views ### How to form the following constraint in cvx? The optimization problem is$$\min_{x\in K} \|h - x\|_2$$where$$K = \{v\in R^n : \exists \lambda \geq 0\ v_1=v_2=\ldots=v_k=\lambda \ \text{and} \ |v_i| \leq \lambda \ \text{for} \ i=k+1,\ldots,n \...
Suppose we have a linear objective function that we want to maximize. All variables are from the set of reals. We have a constraint of the form: \max(x_1,x_2) + \max(x_3,x_4)\leq c\,, \text{ with } ...