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
77 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?
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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: ...
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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 ...
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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 ...
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1answer
82 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 ...
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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
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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 ...
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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: $$\sum_{u, i} (1 + \alpha \cdot r_{ui})(p_{ui} - x_{u}^{T}y_i)^2$$ ...
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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): $$ \frac{1}{N}\sum_{i=1}^N f(x,\xi^i). $$...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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0answers
48 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 $...
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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}))...
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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 ?
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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 ...
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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 ...
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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 ...
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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 ...
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84 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 ...
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1answer
65 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 $t \leq log(det(X))$, ...
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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 ...
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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.
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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
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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 ...
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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 ...
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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
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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 ...
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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 ...
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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}...
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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 ...
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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 ...
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1answer
55 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 ...
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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
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3answers
425 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://...
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3answers
134 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, ...
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0answers
216 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 ...
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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
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1answer
419 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, $...
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1answer
97 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. ...
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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
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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. \...
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0answers
59 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....
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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 ...
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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
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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
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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 ...
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0answers
41 views

Compressed Sensing - CoSaMP algorithm

I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing, I use a first FFT to solve the range ...

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