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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1answer
25 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 FFT spectra are for the flow behind a cylinder. The good one is classified on the basis of how closely spaced the ...
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1answer
35 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 ...
2
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1answer
73 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
19 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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0answers
29 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 ...
2
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1answer
31 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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2answers
66 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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0answers
16 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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0answers
17 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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0answers
37 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 ...
0
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1answer
27 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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0answers
48 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
45 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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38 views

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 ...
4
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2answers
62 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}{...
4
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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 ...
2
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2answers
89 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 ...
3
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2answers
176 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 ...
4
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1answer
81 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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0answers
33 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{...
4
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1answer
69 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 \...
3
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1answer
94 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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0answers
50 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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0answers
18 views

SHREC 2010 Descriptors

I will appreciate if I may find someone how can clarify for me the part regarding the quality of feature descriptor, shown in the figure below: and this screenshot is from the article: SHREC All my ...
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0answers
86 views

Proving convexity of Frobenius norm and correlation function formulations of an optimization problem

I have been working on formulating my requirements in the form of an optimization problem in a multi-output regression setting. Firstly, I would like to make the variables I used in the problem and ...
3
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1answer
62 views

Evaluate 3D Shape Descriptor

I'm trying to create my own 3d shape descriptor, the idea is that how I may evaluate how much my descriptor is well and good? What I checked is that they evaluate descriptors through shape matching, ...
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0answers
59 views

Conjugacy in Non-linear Conjugate Gradient Descent

In linear conjugate gradient method, our goal is to solve the system of linear equations $$Ax = b$$ where A is a symmetric positive definite matrix, and that is equivalent to finding the minimizer of ...
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0answers
20 views

How to use the solution of a multistage stochastic program?

Given a multistage stochastic program, its solution (if it exists) consists of the first decision vector, as well as all the recourse decision vectors for all possible scenarios of an event tree. But ...
8
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1answer
252 views

When training a neural network, why choose Adam over L-BGFS for the optimizer?

More specifically, when training a neural network, what reasons are there for choosing an optimizer from the family consisting of stochastic gradient descent (SGD) and its extensions (RMSProp, Adam, ...
2
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1answer
50 views

Could the convex problem be tackled by CVX?

I want to solve the convex optimization as follows: \begin{align} \underset{X_1,X_2}{\min} &\ -\frac{1}{N}\sum_{i=1}^N\log\det\left(I+H_i^HX_2H_i\right)-\log\left[1+h^H(X_1+X_2)h\right]\\ &\...
2
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0answers
41 views

Fitting a plane with the Prewitt gradient operator

Prewitt gradient operator Show that the Prewitt gradient operator can be obtained by fitting the least-squares plane through the 3 × 3 neighborhood of the intensity function. Hint: Fit a plane to ...
4
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0answers
42 views

Nonlinear least squares optimized Jacobian calculation

I have a nonlinear least squares problem, in which I am trying to minimize residuals which can be divided into four classes: $$ \min_x ||\epsilon(x)||^2 + ||\xi(x)||^2 + ||\delta(x)||^2 + ||s(x)||^2 $$...
1
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1answer
69 views

Prove that the set of maximizers are independent of parameter in the objective function

A maximization problem reads as $$ J(y) = \sum_{k=1}^{K} \sigma_k(y)^q \mathop{\rightarrow}^{y} max$$ where $q \in [1,\infty]$ is a user-defined parameter and functions $\sigma_k, k=\{1,\dots,K\}$ ...
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0answers
51 views

Methods to approximate obective function gradients from point cloud

Problem statement: Assume that I have an objective function $f(x)$ which takes as input a $D$-dimensional vector $x\in\mathbb{R}^D$, and that $f(x)$ is sufficiently smooth. Assume further that I ...
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0answers
67 views

How to approach geographic data interpolation by distance?

let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order. Now I'm ...
2
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1answer
59 views

How to obtain only the value of my variable using scipy.optimize.minimize

when I minimize a function using scipy.optimize.minimize I get a big list of things as a result, but I would like to only get the value of my variable, this is my code : ...
2
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0answers
56 views

Multilevel minimization - boundary conditions

I am interested in minimizing $$min_{x \in R^{n^l}} f^l(x),$$ where $f^l(x)$ is nonlinear objective function arising from discretization of PDE. I would like to use nonlinear multilevel minimization ...
3
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1answer
72 views

Calculate Transformation Matrix between two sensors

My question is if I can calculate the transformation matrix between two sensors. Each sensor provides a $4\times 4$ matrix for every timestep recorded. The sensors are moving and have some noise in ...
3
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2answers
54 views

Optimal line such that maximum points are between an upper and lower boundary

I have some 2D data and would like to find a line $y = mx + b$ such that a maximum number of points from the data is captured within the area between $y = mx + b + margin$ and $y = mx + b - margin$. ...
6
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2answers
177 views

How to solve calculus of variations problems numerically?

For example, how to solve the well-known isoperimetric problem (i.e., to enclose the largest area with a fixed-length curve)? We can simplify things a bit and fix the two ends of the curve at $[a,0]$,...
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0answers
30 views

Method for implementing QP solver with matrix terms?

I am trying to implement (in code) a QP solver for the following equation: $$\min_{u} u^{T} Wu$$ $$s.t. \; \beta u = \tau_{ref}$$ $$ Au \leq b $$ See this document, section 5.1 (Page 35) $u$ is a ...
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0answers
68 views

Ramp least squares estimation

With some given $s$ value, let \begin{equation} \begin{aligned} h(\beta)&=\min(\sum_{i=1}^n(Y_i - X_i\beta)^2, s)\\ &=\sum_{i=1}^n(Y_i - X_i\beta)^2-\max(0, \sum_{i=1}^n(Y_i - X_i\beta)...
2
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1answer
59 views

Python-accessible industry-standard for unconstrained minimization that converges to machine precision?

I have an unconstrained minimization problem of many variables for which I know the gradient exactly. I turned to the conjugate gradient method contained in ...
2
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0answers
47 views

Interesting maxmin mixed integer/real quadratic optimization problem

I have the following problem: $ \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator*{\argmin}{arg\,min} \argmax_{\underset{\lambda_k\in \mathbb{R}}{\sigma_q^2(k)\in \mathbb{R}}} \left[\...
1
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1answer
55 views

ADMM: why does method of multipliers lose decomposability

I am trying to understand intuition of ADMM (alternating direction methods of multipliers). It combines dual ascent and method of multipliers. Downside of method of multiplier is the loss of ...
5
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0answers
96 views

Minimum of quadratic assignment (QAP) with convex objective

Suppose $A,B\succeq0$ and $C\in\mathbb R^{n\times n}$. I am hoping to solve an instance of the following optimization problem: $$ \min_{\textrm{permutation matrices }P} \mathrm{tr}(BP^\top AP+C^\top ...
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0answers
48 views

Least square approximation of a polynomial with a constraint on the derivative in Python

I'm trying to fit a polynomial of the third degree through a number of points. This could be a very simple problem when not constraining the derivative. I found some promising solutions using CVXPY to ...
3
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1answer
106 views

Can I solve a model in GEKKO with Black Box, Simulated Annealing or GA solvers?

I'm trying to use my current GEKKO model with different solvers methodologies. I don't know if I can also use global optimisation solvers as GA, Simulated Annealing o Differential Evolution. I need ...
4
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1answer
40 views

Binary combinatorial optimization with hard to compute costs

I have a combinatorial problem regarding the optimal placement of sensors. I want to find the optimal placement of $N$ sensors, given $M$ possible locations, $N < M$. Right now I'm working with ...
6
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1answer
96 views

Optimization algorithm / approach for suggesting what goods to buy and sell in a marketplace?

A toy problem would probably be best to explain it this. Let's say we have 100 people, each with 4 unique types of items (to simplify things, let's say it's the same four types of items for each ...

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