Questions tagged [optimization]
This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.
910
questions
2
votes
0answers
28 views
Cyipopt fails to converge for NLP problem which fmincon() can solve
I'm currently trying to implement a python script for solving a constrained nonlinear optimization problem with ~800 variables and 2 constraints, one linear and one nonlinear. There already exists a ...
-1
votes
0answers
40 views
Numerical difficulties solving 1D steady-state, real gas pipe-flow problem (I think) [closed]
I am trying to implement a 1D, steady-state, real gas (compressibility factor) pipe flow model in Python using Pyomo + SCIP. It basically amounts to solving a DAE system. The formulation is an adopted ...
2
votes
0answers
31 views
Calculating a submanifold of minimal values
I have a (numerical, noisy) function $f$ that I'd like to optimize (in 3 < dimension < 10).
The function $f$ has a fairly prominent valley/ravine structure due to physical symmetries present in ...
2
votes
1answer
37 views
Python solvers for MINLP in Pyomo in Google Colab
I am looking for a MINLP solver that works with Pyomo models which can be used in the Google Colab environment. I have already found MindtPy but it doesn't work in google colab.
3
votes
0answers
90 views
How amenable is this 2D Frenkel–Kontorova-like energy minimization problem in Python to the use of a modest PC + GPU? (Heavy reliance on indexing)
@Richard's answer to Going to try to move some of my scipy/numpy calculation to a new GPU, how to avoid disappointing results? is quite helpful, and as promised I've added a simple running example ...
9
votes
1answer
417 views
How to find the smallest ellipse covering a given fraction of a set of points?
I have a set of points $P$ and want to find the ellipse with the smallest area that covers at least a fraction $f$ of these points. How can I do this?
These questions ask the same thing, but folks ...
3
votes
1answer
175 views
Going to try to move some of my scipy/numpy calculation to a new GPU, how to avoid disappointing results?
update: I've refactored the question based on helpful advice in the linked meta.
I'm a heavy user of Python's NumPy and SciPy (and not much else) and for years I could run anything I need on my laptop....
12
votes
2answers
1k views
How do I find the minimum-area ellipse that encloses a set of points?
I have a set of points that resembles more of an ellipse than a circle. I implemented the optimization formulation below and the solution gives a circle. I tried with various initial values, still to ...
8
votes
2answers
113 views
Approximating the boundary between two sets of points (in 2D): Fitting a region
Given two sets of points $p_{\text{in},i}$ and $p_{\text{out},j}$ inside and outside of what I intuitively call a "region", I would like to estimate and describe the boundary of this region. ...
1
vote
0answers
106 views
How to solve the minization problem with $Z^{T}Z=I$
I have the following problem
$$\underset{Z}{\min}\left\|X-AZBH\right\|_F^2+\left\|H-B^{T}Z^{T}A^{T}X\right\|\\
\text{subject to } Z^{T}Z=I$$
How to solve the variable $Z$?
2
votes
1answer
114 views
Is solving QP easier than a QCQP with linear objective?
Is solving a $QP$ (i.e.: quadratic program, hence a quadratic objective function with linear constraints) easier than solving a $QCQP$ (ie.: quadratic constrained quadratic problem) with linear ...
1
vote
1answer
85 views
Finding the root of an equation (divergence at some points)
I am trying to solve this equation for $v_{Sl}$ in the range $[0.001,1]$ to obtain the values of $\delta_l$. I have tried Fsolve with python, which gives results ...
6
votes
0answers
111 views
FEM : energy minimization VS PDE solving
Engineering FEM
When I studied engineering, I learned the traditional approach for finite elements for elasticity. The point was to solve the PDE $-div(\sigma)=f$ as:
Multiply your PDE with a test ...
2
votes
1answer
113 views
Difference between asymptotic and non-asymptotic convergence in optimization?
I am reading some optimization methods and I am facing some issues with two terms "asymptotic and non-asymptotic convergence". What is the difference between them?
2
votes
1answer
88 views
Formulating this optimization problem
Suppose I want to minimize below objective function
$\sum | g(x_i) \cdot I_{g(x_i)<0} |^2$
i.e, the latter penalty terms like $ |g(x_i)|^2 $ are only computed when $g(x_i)<0$. $|g(x_i)|^2$ are ...
5
votes
2answers
108 views
Optimizing a quadratic form integral over unit sphere
I have an optimization problem, which is to maximize the following integral over the unit sphere:
$$
\max_B \int d\Omega \mathbf{f}^{\dagger}(\theta,\phi) (B^{\dagger} + B) \mathbf{f}(\theta,\phi)
$$
...
3
votes
1answer
102 views
Parameters estimation with fewer variables than parameters
I am trying to estimate parameters, 4 of them, by fitting a system of 3 ordinary differential equations.
I am using a model published that was using 3 parameters and gave a good fit to the data, and I ...
0
votes
0answers
61 views
Comparing minimas of two different functions
The goal is to find vectors $x_u$ and $y_i$, both of the same length $f=64$, and to do this the following loss function is minimized:
$$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$
...
3
votes
0answers
48 views
Sample Average Approximation vs. Numerical Integration
To calculate the expected value of objective functions, we have two choices:
Sample Average Approximation (SAA):
$$
\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).
$$
Numerical Integration (e.g., Monte Carlo ...
0
votes
1answer
61 views
Expressing a Constraint in an optimization problem
If I have a vector of M "continuous" decision variables (say it is called x) , and if I want a constraint to express that only one of them is allowed to have a nonzero value (i.e. no more ...
1
vote
0answers
72 views
Binarization for optimization problems
I have a nonlinear mixed-integer optimization problem, and because of very high complexity when solving it using methods like Branch and Bound, I resorted to solve it using alternating method and ...
2
votes
0answers
50 views
Adding a "cost term" to a linear regression, so solution values are minimized
I'm using Python's optimize.lsq_linear method to run a linear regression with the bounds set between 0% and 100% power usage.
...
2
votes
0answers
72 views
Efficient solver of a Integer programming
I am solving an Integer programming using MATLAB, yet the efficiency is low.
Here is the problem:
Suppose $v$ is a $N \times 1$ vector. For $v_i \in v$, $v_i \in \{0,1\}$.
$D$ is a 0-1 matrix, which ...
1
vote
0answers
61 views
Maximizing $l_1$-normalized entropy using CVXPY
Suppose that $x = (x_1, ..., x_n)$ is a vector of variables and I would like to maximize the Shannon entropy of $\frac{|x|}{||x||_1}$ (i.e. the vector of absolute values of $x_i$, normalized to have $...
0
votes
0answers
11 views
Optimal Time Series Weight for Quantile Estimation
Given a time series, $x_1$, $x_2$, ..., $x_t$, .... I want to solve for
$$\mathrm{min}_{w_1, w_2, ..., w_m}\rho(x_t-\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t-m}; w_{t-1}, w_{t-2}, ..., w_{t-m}))...
-2
votes
1answer
71 views
How to get 10 in computer science, using the number 4 exactly four times, and two signs exactly and two operation + exactly? [closed]
How to get 10 in computer science, using the number 4 exactly four times, and two signs exactly and two operation + exactly ?
1
vote
0answers
31 views
constrained zero-sum two person game
Finding the saddle point of a constrained zero-sum two-person game is equivalent to a resolution of primal-dual programs (with bi-linear objective function).
I am looking for a free solver to compute ...
0
votes
0answers
41 views
Can this volume intgral be expressed as a convex function?
This question is related to the following:
https://math.stackexchange.com/q/4151405/685910 - the context is summarized below for clarity.
In the setting of convex optimization, I am looking for a ...
1
vote
0answers
57 views
Constrained optimization for non-linear equations in octaveGNU
I have installed Optim1.6.1 package. I would like to solve a system of equations in non linear finite element analysis using constraints as u=1 at certain nodes. u=0 at certain nodes. Typically I find ...
0
votes
0answers
51 views
Equivalence between zero sum games and linear program
It is well known that you can use the algorithm for finding the equilibrium of a Zero-sum game to solve a linear program. In particular, you can take a LP and reduce it to a zero-sum game, and use the ...
0
votes
0answers
57 views
Relative interior requirement in Slater's condition
I'm reading Convex Optimization by Boyd and Vandenberghe. This is how they describe Slater's condition:
What I don't understand is why it is necessary to enforce that $x$ be in the relative interior ...
6
votes
0answers
88 views
continuous analogues of Newton's method
Suppose we want to minimize some convex functional $J(u)$ where $u$ lives in some Banach space $V$.
The classical Newton method
$$\mathrm d^2J(u_n)(u_{n + 1} - u_n) = -\mathrm dJ(u_n)$$
can be viewed ...
2
votes
1answer
80 views
Log-Determinant constraints in SDP
This is a belated follow up to my question here, because I didn't want to tack questions onto questions.
According to the Mosek documentation here, one possibility for expressing $t \leq log(det(X))$, ...
1
vote
0answers
56 views
tiny typo in Numerical Recipes Eq. 9.4.6 [closed]
The Numerical Recipes Forum http://numerical.recipes/forum/ is closed, so I will record a tiny typo here for the benefit of others who may wonder about this. (This typo is not in the software, but ...
1
vote
1answer
58 views
What is the best cooling and flippling schedule in simulated annealing?
I've noticed that some heuristics for it on my problem which work surprisingly well. I guess it ought to be systematically studied although I cannot find guides or overviews for it.
0
votes
0answers
62 views
Optimization algorithm to find coinciding root and minimum
Are there any optimization algorithms aimed at finding a coinciding root and a (local) minimum of a multi-variable function f. Say it is known analytically that ...
7
votes
1answer
197 views
How does the number of function calls in BFGS scale with the dimensionality of space?
Question
Is there any estimate for the scaling of the number of function calls in BFGS-optimization with the dimensionality of the search space? Specifically I am assuming a (free) expression for the ...
0
votes
0answers
60 views
How to efficiently perform this 2D integral in Quadpy?
I need to integrate a function defined in 2Dims (z and radius r), for which I don't have an expression.
I can just query the ...
0
votes
0answers
48 views
Help with finding an objective function for optimization
Im working in comsol and needed help figuring out the objective function for the following situation (Comsol does have multiple objective function option as min max or sum of)
I have 7 batteries ...
4
votes
3answers
185 views
Algorithms to generate spherical codes
A spherical code, specified by the parameters $(n,N,t)$, is a set of $N$ coordinates on the $n$-dimensional unit hypersphere such that the set of dot products between any two unit vectors from the ...
0
votes
2answers
90 views
Validating that a code is a good spherical code
Apologies if this is a trivial question. If that is the case I imagine I would benefit from someone explaining where my understanding is lacking.
I am having some trouble interpreting the (putatively ...
0
votes
0answers
46 views
Blown-up iterates in Gauss-Newton method
I am working on a non-linear least squares problem with standard form, in which I need to calibrate a parameter vector $\Theta$ to a set of inputs $\mathbf{x}$ and outputs $\mathbf{y}$:
$$\begin{align}...
5
votes
0answers
91 views
How to find a lot of (if not all) local minima / critical points of a function?
Briefly stated, I would like to find "all" local minima / critical points of a function.
This function comes from the discretization of a continuous problem with infinitely many degrees of ...
-1
votes
1answer
35 views
Interpretation of error between Hessian approximation and real Hessian - Quasi-Newton Method
$$ ||I- H_{k}^{BFGS}\nabla^{2}f(x_{k})||_{2}$$
, where $H_{k}$ is the inverse of hessian approximation at each iteration.
I am given this expression to assess the error in Hessian approximation in ...
-1
votes
1answer
79 views
Is there an overview of the runtime speed up of LP/MIP solvers throughout the years?
whenever I read papers on OR that use an LP/MIP approach, they include the time solver used, as well as the version and the year. I would like to know how much faster the same experiment would be ...
1
vote
0answers
35 views
Energy cannot decent during optimization despite non-zero gradient
Assume we have an (at least) 2nd-order differentiable energy $f(x), x\in R^n.$ And $n$ is very big. Mathematically, I think it is impossible to find a point $\bar{x}$ where the energy cannot be ...
4
votes
3answers
550 views
Which absolute and/or relative stopping criteria do use for Newton's method?
I saw many stopping criteria for Newton's method all around Web and books.
Some are defined from the residuals:
of either current iteration only:
$$
\|f(\mathbf{x}^{(k)})\| \leq \epsilon
$$
(https://...
1
vote
3answers
160 views
How can we solve the normal equations with limited memory?
I was asked this open ended question in an interview once:
How would you find a solution to the normal equations with limited memory?
Unlike Solving sparse least squares system with limited memory, ...
0
votes
0answers
285 views
similar function as fmincon in python?
I am trying to solve an optimization problem where I do not have the analytic form of the objective function. I am doing analysis by FEM to find a value for displacement in each iteration but I don't ...
0
votes
0answers
67 views
L2 norm optimization problem
I have an optimization problem where i need to find an image x, that is very close to x' such that:
monitor(x') is valid but monitor(x) is invalid. (output is valid
when the neural network output is ...
