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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46 views

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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31 views

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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30 views

Could not get expected result?

I am trying to solve the example 3.3 in this book. ...
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24 views

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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1answer
61 views

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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1answer
54 views

Reformulating a convex optimization problem with $x \mapsto \max(x,0)$ in the constraint

I am wondering if there is a well-known transformation allowing one to solve convex optimization problems of the form $$\begin{array}{ll} \underset{x}{\text{maximize}} & r^T x\\ \text{subject to} &...
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62 views

Which algorithm is capable of solving a combinatorial optimization problem like this?

The problem I have at hand is a regression problem where each of $p$ inputs, $x_1, x_2, x_3, \cdots, x_p$, needs to undergo a variable transformation using one of $q$ basis functions from a set of ...
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79 views

N-dimensional optimization of moments of distribution function

Let's say I have a bag of marbles. Each marble has several attributes (color, diameter, surface roughness, weight). I know that there is a statistical relationship between various marble attributes ...
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50 views

Quadratic optimization with nonlinear vector term

I wish to minimize the quantity $$W=1/2x^TAx-x^Tg(y)$$ with respect to $x$ and $y$, which are vectors of unknowns. $A$ is a sparse square symmetric positive definite matrix and $g(y)$ is a vector with ...
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63 views

Derivative-free ill-conditioned non-linear least squares

I am looking for a package which can solve (non-linear) least squares problems without the use of derivatives (because of an expensive model), but which also deals with ill-conditioning well (such as ...
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42 views

How to speed up the Mixed-Integer Quadratic Program process?

Currently, I am solving a problem in the format: M is an integer as well. The problem that troubles me is that X is a vector in {0,1} with a size of 7000. I use the solver in https://github.com/...
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37 views

implementation of shell elements in a topology optimization algorithm

I am working on developing a topology optimization solver based on the finite element method and I want to add a triangular shell element in it. I used the classic finite element method but I didn’t ...
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30 views

What is the generalization of the resource allocation problem I'm dealing with here?

I'm dealing with a problem as follows: I have a finite set of money 𝑚 to spend over 𝑟 different raffles, and I need to spend approximately to my budget, with the goal of maximizing my probability ...
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357 views

When and when not to use automatic differentiation

I am just learning (more) about automatic differentiation (AD) and at this stage it kind of seems like black magic to me. The second paragraph of its Wikipedia article makes it sound too good to be ...
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1answer
84 views

Solve two-player game - minimize the l-infinity norm of a matrix-vector product

I have a matrix $M$ with non-negative real entries, and I would like to minimize the objective function $$\Phi(v) = \|Mv\|_\infty,$$ where $v$ is constrained to be a probability vector, i.e., $v_1+\...
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2answers
260 views

Jacobians with automatic differentiation

I have an objective function F: Nx1 -> Nx1, where N>30000. There are many sparse matrix/tensor multiplications in this function, so taking an analytic Jacobian by paper and pen is cumbersome. ...
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32 views

Convergence of Truncated Newton for non-convex Hessian

I was wondering if anyone could enlighten me about the convergence properties of the truncated newton method in case of a non-positive definite hessian $\nabla^2 f = H$. From the Book 'Numerical ...
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2answers
104 views

Optimization of expensive model with many parameters

I have a physical model which takes $\sim50$ parameters and gives $\sim2000$ outputs taking tens of minutes to run. I need to optimize these parameters to give outputs as close as possible to data. ...
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18 views

Benchmark instances for directed 3-Cycle cover

The directed 3-Cycle cover asks for a vertex-covering set of oriented cycles with at least three vertices per cycle such that every vertex is covered by exactly one cycle. I have scrutinzed the ...
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29 views

Estimating the dimension of a solution space in nonlinear least squares

Suppose I have a nonlinear least squares problem, $$ \min_{\mathbf{x}} || \mathbf{f}(\mathbf{x}) ||^2 $$ with $n$ residuals and $m$ parameters, so that $\mathbf{x} \in \mathbb{R}^m$, and $\mathbf{f} \...
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33 views

Non-negative Least Squares to perform Inverse Laplace with weights

I'm trying to perform the inverse Laplace transform of a (noisy) dataset $y_i$ using Tikhonov regularization: $$\min \sum_{i=1}^{N} \left(\int_0^\infty e^{-s_i t} f(t) \, dt - y_i \right)^2 - \lambda^...
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18 views

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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1answer
37 views

Norm constraint in CVXPY

I'm trying to implement the algorithm outlined in https://arxiv.org/abs/1211.5608 on a small scale. I have a linear operator $\mathcal{A}$ which is defined as $$\text{trace}(A^*_l(hm^*))$$ where $$A_l ...
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1answer
26 views

How to check curvature of a vector valued function

In terms of numerical optimization, the newton-rapson method requires a pos. definite Hessian $\nabla^2f$ respectively pos. curvature for computing the next step $p_k$ by solving $$\nabla^2 f p_k = -\...
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1answer
25 views

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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1answer
51 views

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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1answer
95 views

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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1answer
137 views

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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1answer
40 views

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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1answer
81 views

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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1answer
20 views

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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2answers
98 views

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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1answer
35 views

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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72 views

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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23 views

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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18 views

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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39 views

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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1answer
31 views

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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53 views

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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1answer
48 views

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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2answers
65 views

MInimizing cost function using iterative search for a minimum method

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}{...
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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 ...
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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 ...
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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 ...
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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^...
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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{...
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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 \...
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1answer
121 views

What are the advantages of Level Set method in topology optimization?

I am studying the different topology optimization methods. There are numerous resources out there but when it comes to comparing different algorithms, in terms of strengths and weaknesses most of ...
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56 views

Are there unproblematic max constraints when modelling problems as Linear Programs?

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 } ...

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