Questions tagged [optimization]
This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.
900
questions
6
votes
0answers
80 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
78 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?
-1
votes
0answers
27 views
Can constants and parameters in a Gekko model be simply Python variables?
I'm new to Gekko and I noticed that Gekko will still run even if I don't define fixed values in my model as Gekko constants and parameters. For example, this code still runs and gives an answer:
...
-1
votes
0answers
24 views
the convergence of the iterative algorithm has a major problem
In order to solve an optimization problem, I divided the main problem into two sub-problems. The two sub-problems require to be solved iteratively until the algorithm converges.
I use the bi-section ...
-1
votes
0answers
27 views
Do we need smallest vectors to obtain the optimized solution in Gradient Descent?
I'm new to topics about optimization. I am currently reading about Steepest Descent Method in Gradient Descent optimization.
I saw this equation where we need to find a new iterate with an initial ...
2
votes
1answer
83 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
102 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
58 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:
$$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$
...
1
vote
0answers
25 views
Sample Average Approximation vs. Numerical Integration
In the sense of the calculation of the expected value of objective functions, we have two choices to evaluate the value; 1. Sample Average Approximation (SAA):
$$
\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).
$$...
0
votes
0answers
83 views
Find coefficients in general second order differential equation
Suppose you have a system that can be described via the following equations of motion:
$$\ddot{y}+\delta(t)\dot{y}+\alpha(t) y = \gamma\sin(\omega t)$$
The functions $\delta(t)$ and $\alpha(t)$ are ...
0
votes
1answer
60 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
65 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
38 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
69 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
49 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
$$\mathrm{min}_{w_1, w_2, ..., w_m}\rho(x_t-\mathrm{Quantile}(q; x_{t-1}, x_{t-2}, ..., x_{t-m}; w_{t-1}, w_{t-2}, ..., w_{t-m}))...
-2
votes
1answer
63 views
How to get 10 in computer science, using the number 4 exactly four times, and two signs exactly and two operation + exactly? [closed]
How to get 10 in computer science, using the number 4 exactly four times, and two signs exactly and two operation + exactly ?
0
votes
0answers
41 views
Can this volume intgral be expressed as a convex function?
This question is related to the following:
https://math.stackexchange.com/q/4151405/685910 - the context is summarized below for clarity.
In the setting of convex optimization, I am looking for a ...
1
vote
0answers
55 views
Constrained optimization for non-linear equations in octaveGNU
I have installed Optim1.6.1 package. I would like to solve a system of equations in non linear finite element analysis using constraints as u=1 at certain nodes. u=0 at certain nodes. Typically I find ...
0
votes
0answers
47 views
Equivalence between zero sum games and linear program
It is well known that you can use the algorithm for finding the equilibrium of a Zero-sum game to solve a linear program. In particular, you can take a LP and reduce it to a zero-sum game, and use the ...
0
votes
0answers
38 views
Relative interior requirement in Slater's condition
I'm reading Convex Optimization by Boyd and Vandenberghe. This is how they describe Slater's condition:
What I don't understand is why it is necessary to enforce that $x$ be in the relative interior ...
6
votes
0answers
85 views
continuous analogues of Newton's method
Suppose we want to minimize some convex functional $J(u)$ where $u$ lives in some Banach space $V$.
The classical Newton method
$$\mathrm d^2J(u_n)(u_{n + 1} - u_n) = -\mathrm dJ(u_n)$$
can be viewed ...
2
votes
1answer
66 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
55 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
58 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 ...
6
votes
1answer
156 views
How does the number of function calls in BFGS scale with the dimensionality of space
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 gradient ...
0
votes
0answers
46 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
43 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
169 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
85 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
44 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
90 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
34 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
56 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
430 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
135 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
218 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
65 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 ...
0
votes
1answer
423 views
Levenberg-Marquardt Algorithm for Black-box optimizations
I would like to create an optimization solution for black-box software calculations. Currently, I am using the Levenberg-Marquardt algorithm to update a vector of parameters, $\beta$, with residuals, $...
0
votes
1answer
98 views
How to generate neighbors for simulated annealing
I am learning about simulated annealing algorithm and want to create a general purpose one for optimizing continuous functions.
The problem I have is how to generate the neighbor points as candidates. ...
2
votes
0answers
84 views
Finding the extrema of a transition probability function for a quantum walker on a graph
The goal
Implement some Python code to find the extrema points of a function that is strongly oscillating.
The background
Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
4
votes
1answer
162 views
SCP (Sequential Convex Programming) vs SQP (Sequential Quadratic Programming)
Can someone explain me at a high level the difference between an SCP and an SQP to solve a nonlinear (nonconvex) program?
Assume my problem is something like
$$\min\limits_x. \quad f(x)$$
$$s.t. \...
3
votes
0answers
60 views
What is this QR-factorization-based preconditioning called?
I have recently started to delve into someone else's code, and there is a part in there I don't quite understand. The authors of the code use some form of pre-conditioning to speed up the optimization....
2
votes
0answers
88 views
Black box optimization
I have a simulation which gives a scalar result depending on the choice of some continuous design variables. I am trying to minimize the output of the simulation. As a first step, I want to study the ...
1
vote
0answers
19 views
Minimize MAE for sum of powers
The model is
$$y_i=\beta\big(x_{i1}^\alpha+x_{i2}^\alpha+...+x_{im_i}^\alpha\big)+\epsilon_i\textrm{ for }i=1, 2, ..., n$$
I want to minimize the MAE, i.e.
$$\Sigma_{i=1}^n{\big|y_i-\beta\big(x_{i1}^\...
3
votes
1answer
100 views
Nonlinear root solving libraries which accept a Jacobian in band-storage
I'm in search for a library for solving large systems of non-linear equations, similar to MINPACK, but unlike MINPACK, can accept a Jacobian in band-storage.
My Jacobian is sometimes not invertible, ...
2
votes
0answers
132 views
Parametric nonlinear programming
I believe, I have a parametric nonlinear optimization problem.
The non-convex constraints depend on some parameters, and I seek a solution that satisfies these constraints for all parameters in a ...
