Questions tagged [optimization]
This tag is intended for questions on methods for the (constrained or unconstrained) minimization or maximization of functions.
879
questions
6
votes
0answers
78 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
49 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
54 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
52 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
143 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
25 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
40 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
131 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
81 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
36 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 $\mathbf{y}$:
$$\begin{align}...
5
votes
0answers
86 views
How to find a lot of (if not all) local minima / critical points of a function?
Briefly stated, I would like to find "all" local minima / critical points of a function.
This function comes from the discretization of a continuous problem with infinitely many degrees of ...
-1
votes
1answer
32 views
Interpretation of error between Hessian approximation and real Hessian - Quasi-Newton Method
$$ ||I- H_{k}^{BFGS}\nabla^{2}f(x_{k})||_{2}$$
, where $H_{k}$ is the inverse of hessian approximation at each iteration.
I am given this expression to assess the error in Hessian approximation in ...
-1
votes
1answer
37 views
Is there an overview of the runtime speed up of LP/MIP solvers throughout the years?
whenever I read papers on OR that use an LP/MIP approach, they include the time solver used, as well as the version and the year. I would like to know how much faster the same experiment would be ...
1
vote
0answers
35 views
Energy cannot decent during optimization despite non-zero gradient
Assume we have an (at least) 2nd-order differentiable energy $f(x), x\in R^n.$ And $n$ is very big. Mathematically, I think it is impossible to find a point $\bar{x}$ where the energy cannot be ...
4
votes
3answers
238 views
Which absolute and/or relative stopping criteria do use for Newton's method?
I saw many stopping criteria for Newton's method all around Web and books.
Some are defined from the residuals:
of either current iteration only:
$$
\|f(\mathbf{x}^{(k)})\| \leq \epsilon
$$
(https://...
0
votes
3answers
108 views
How can we solve the normal equations with limited memory?
I was asked this open ended question in an interview once:
How would you find a solution to the normal equations with limited memory?
Unlike Solving sparse least squares system with limited memory, ...
0
votes
0answers
66 views
similar function as fmincon in python?
I am trying to solve an optimization problem where I do not have the analytic form of the objective function. I am doing analysis by FEM to find a value for displacement in each iteration but I don't ...
0
votes
0answers
56 views
L2 norm optimization problem
I have an optimization problem where i need to find an image x, that is very close to x' such that:
monitor(x') is valid but monitor(x) is invalid. (output is valid
when the neural network output is ...
0
votes
1answer
163 views
Levenberg-Marquardt Algorithm for Black-box optimizations
I would like to create an optimization solution for black-box software calculations. Currently, I am using the Levenberg-Marquardt algorithm to update a vector of parameters, $\beta$, with residuals, $...
0
votes
1answer
47 views
How to generate neighbors for simulated annealing
I am learning about simulated annealing algorithm and want to create a general purpose one for optimizing continuous functions.
The problem I have is how to generate the neighbor points as candidates. ...
2
votes
0answers
81 views
Finding the extrema of a transition probability function for a quantum walker on a graph
The goal
Implement some Python code to find the extrema points of a function that is strongly oscillating.
The background
Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
4
votes
1answer
78 views
SCP (Sequential Convex Programming) vs SQP (Sequential Quadratic Programming)
Can someone explain me at a high level the difference between an SCP and an SQP to solve a nonlinear (nonconvex) program?
Assume my problem is something like
$$\min\limits_x. \quad f(x)$$
$$s.t. \...
3
votes
0answers
52 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
82 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.
$$\Sigma_{i=1}^n{\big|y_i-\beta\big(x_{i1}^\...
3
votes
1answer
62 views
Nonlinear root solving libraries which accept a Jacobian in band-storage
I'm in search for a library for solving large systems of non-linear equations, similar to MINPACK, but unlike MINPACK, can accept a Jacobian in band-storage.
My Jacobian is sometimes not invertible, ...
2
votes
0answers
132 views
Parametric nonlinear programming
I believe, I have a parametric nonlinear optimization problem.
The non-convex constraints depend on some parameters, and I seek a solution that satisfies these constraints for all parameters in a ...
0
votes
0answers
33 views
Compressed Sensing - CoSaMP algorithm
I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing, I use a first FFT to solve the range ...
1
vote
1answer
98 views
How to best code a problem with scipy, cvxpy or Convex.jl with given generated data
I have a curve fitting problem of the form:
$$
\textbf{y} = f(\textbf{x}, a,b,c,d) + \varepsilon
$$
$$
f(x, a,b,c,d) = \frac{b}{e^{x\cdot a}+c}+d
$$
with the constraint
\begin{equation}
\begin{aligned}...
5
votes
0answers
79 views
Can automatic differentiation be used on the parameters of an optimization problem?
If I wanted to perform an optimization using a Newton-based solver where the Hessian and gradient of a function are known analytically, and then use a package such as Adept to compute a Jacobian ...
0
votes
1answer
164 views
How to compare 2D vector fields and minimize the difference?
I want to compare the field of two electrical currents and compare the resulting field to a magnetic dipol field and find magnetic momentum that minimizes the difference of the two fields.
My current ...
3
votes
1answer
119 views
A notion of resolution in inverse problems
Suppose I have a linear inverse problem of the form:
\begin{align}
Ax=b
\end{align}
I would like to reconstruct $x$ from the measurement $b$ via the objective
$$\min_x\{\vert\vert Ax-b\vert\vert^2_2+\...
1
vote
0answers
274 views
Minimax optimization with an oracle
I have an optimization problem of the following form: $$\min_y\left[\max_x f(x,y)\right].$$ It is fairly straightforward to minimize $f(x,y)$ over $y$ with $x$ fixed, and similarly to maximize $f(x,...
2
votes
0answers
84 views
How to derive the adjoint sensitivity equations for a least squares objective function gradient
The Problem
I would like to determine the gradient of a least squares objective function which depends on a vector of 40 parameters $p$, and the solution of a system of 32 differential equations. In ...
1
vote
1answer
106 views
Optimization on the multinomial manifolds of stochastic non-square matrices
Thanks for note! So I have an optimization problem with simple form but the decision variable is a large-scale matrix. My problem is similar to a existing problem here about multinomial manifolds and ...
0
votes
1answer
74 views
How can I deal with optimization problems that have a sum of functions of Z as a constraint when Z is the quantity to be minimized?
I have a problem where I have to minimize a certain quantity $Z$ subject to the following constraints:-
$w_1 + w_2 + w_3 = 1$
$\frac{f_1(w_1*Z) + f_2(w_2 * Z) + f_3(w_3 * Z)}{Z} >= k$
where $k$ ...
4
votes
0answers
64 views
Optimize linear equation using inner products and subject to L1 norm
I have a linear system of the form $A x = b$ where $A$ and $b$ are known, $A$ is "square", and $\lvert b \rvert_1 = \lvert x \rvert_1 = 1$. Unfortunately, I am working in a framework that ...
1
vote
1answer
54 views
Constraint programming problem with conditional constraints and some unknown indicator variables
I have an interesting little problem that I believe can be formulated in terms of optimization or constraint programming. I have a few dozen variables $a$, $b$, $c$ ... and a set of constraints that ...
2
votes
2answers
131 views
L1 least squares minimization with a sparse matrix
I have the following problem:
$$\min_{x\in \mathbb{R}^n}\|Ax-b\|_1$$
where the matrix $A$ is large and sparse. I am looking for methods/code that can minimize this efficiently. References are very ...
2
votes
0answers
29 views
Scaling tensor approximation by symmetric tensor decomposition with SciPy's L-BFGS-B
I am trying to approximate a symmetric tensor of which the values are in the range of [1e-7,1e-4], by a symmetric tensor decomposition of lower rank. For this I am using the L-BFGS-B method in SciPy's ...
5
votes
0answers
133 views
Inverse problem with uncertain forward operator
Suppose I want to solve a linear inverse problem. In this example we take a convolution with the kernel:
$$\frac{1}{(y^2+z^2)^{3/2}}$$
We only take a fixed $z$ for the computation and convolve with ...
2
votes
2answers
61 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 ...
0
votes
1answer
95 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 ...
2
votes
1answer
85 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
$$\begin{array}{ll} \underset{x}{\text{maximize}} & r^T x\\ \text{subject to} &...
0
votes
0answers
69 views
Which algorithm is capable of solving a combinatorial optimization problem like this?
The problem I have at hand is a regression problem where each of $p$ inputs, $x_1, x_2, x_3, \cdots, x_p$, needs to undergo a variable transformation using one of $q$ basis functions from a set of ...
1
vote
0answers
88 views
N-dimensional optimization of moments of distribution function
Let's say I have a bag of marbles. Each marble has several attributes (color, diameter, surface roughness, weight).
I know that there is a statistical relationship between various marble attributes ...
1
vote
0answers
51 views
Quadratic optimization with nonlinear vector term
I wish to minimize the quantity $$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 ...
0
votes
0answers
71 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 ...
1
vote
0answers
67 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/...
