Questions tagged [constraints]
For questions about computationally solving a problem subject to some constraints on the solution. For optimizations, apply the more specific [constrained-optimization] tag instead.
45
questions
2
votes
0answers
80 views
Hanging nodes in deal.ii tutorials: how is the continuity constraint imposed?
While looking at step6 of deal.ii tutorials, I decided to try to understand how the constraints coming from hanging nodes are imposed. So I started by watching video lecture 16 by prof. Bangerth
As ...
2
votes
0answers
32 views
Differences in using Clausius-Duhem inequality vs Principle of Virtual Work/Power in derriving constitutive equations?
I am a novice getting my toes wet in continuum mechanics and nonlinear elasticity. I have seen papers that use both approaches in developing constitutive connections to compliment balance equations of ...
1
vote
1answer
184 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}...
1
vote
1answer
333 views
Is there a way to bound the values of a variable when using scipy.integrate.solve_ivp in python?
I want to solve an IVP in python with two variables, x and u, but I need the values of u to be between 0 and 1. Right now it is giving me a solution with negative values for u. Here is the code I have....
1
vote
1answer
66 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 ...
3
votes
1answer
580 views
Setting up optimization problem in GEKKO
I have the following dynamical system,
$\frac{d \phi}{dt} = -M^TDM\phi \tag{1}\label{1}$
$\frac{d \hat\phi}{dt} = -M^T\tilde{D}M\hat \phi \tag{2} \label{2}$
$\eqref{1}$ represents the exact ...
0
votes
0answers
97 views
Constraining the total volume in Finite Element Methods
I have a diffusion problem which can be broken down to be:
$-\Delta u = f(u) $ on $\Omega ~/~ \Omega_{int}$
$u = 1$ on $\Omega_{int}$
Note that this is an internal Dirichlet constraint to the ...
1
vote
1answer
691 views
sum of absolute difference constraint in optimization problem
I am writing a model for an optimization problem. I need to write the following constraint:
$$\sum^{N - 1}_i \lvert (a_i - a_{i+1}) \rvert \leq 2\, .$$
How to write this constraint (or linearize)?
...
-1
votes
1answer
25 views
Semi-Definite relaxation of non-linear constraint?
I am implementing an optimization problem using semi-definite approach. One of my constraints is of following form
$ trace(A∗X)−(k∗trace(A∗X))+(k∗\sqrt {(trace(B∗X)} )==0$
where k is a constant, A ...
2
votes
0answers
403 views
What is the mathematical and physical principle behind of RBE2 element？
I am writing a 3d linear finite element code to solve the standard linear elasticity equation on a tetrahedron mesh of a gearbox. Notice that, the two rectangular plates above the gearbox are fixed, ...
2
votes
0answers
30 views
Domain for convex perspective function
The perspective of a function $f : \mathbb{R}^n \to \mathbb{R}$ is the function $g: \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}$ where $g$ is defined as $$g(x,t) = tf(x/t)$$ with $$\mathbf{\text{dom}...
2
votes
1answer
46 views
Constraints 'exactly/at most one non-zero element' without binary variables
In a much larger MINLP problem, I have set of variables $\{a_{ij}\}_{m,n}$, such that $0 \leq a_{ij} \leq 1 $ for all $i$, $j$, which I could think of as a matrix, for which I have two requirements:
...
0
votes
1answer
933 views
Defining a soft constraint in cvxpy
I am using cvxpy to do a simple portfolio optimization.
I implemented the following dummy code
...
1
vote
2answers
105 views
Making difference of log constraints convex
I have the discrete likelihood estimation problem $\max \sum m_i\log p_i $ where $m$ is a given vector of length $n$. The constraints are $0 \preceq p \preceq 1$, $\sum_{i=1}^n p_i = 1, $ and one ...
3
votes
1answer
644 views
Linear constraints for L-BFGS-B
I know L-BFGS-B only supports simple box constrains of the form: $l_i \leq x_i \leq u_i$, where $l_i$ and $u_i$ are constants. For my specific optimization problem, I need to specify some simple ...
6
votes
1answer
794 views
Constrained simulated annealing
Simulated annealing is a useful technique for finding near-optimal solutions to combinatorial problems. I have found a lot of tutorials on implementing the basic algorithm, but miss a general guide as ...
1
vote
1answer
601 views
Trajectory optimization for smoothness
I want to achieve the following in 2D (and without obstacles):
Given start position A and end position B, generate the path between the two points that optimizes a cost function that depends on total ...
1
vote
0answers
253 views
the augmented global stiffness matrix is not positive semi-definite using Lagrange Multipliers method within FEM
The augmented global stiffness matrix is not positive semi-definite when using Lagrange Multipliers method to enforce boundary constraints on a simple square domain of integral form:
I am considering ...
6
votes
1answer
2k views
Newton's method with box-constraints
I have to use an iterative method (Newton-Raphson, modified Newton and Broyden) to solve a system of nonlinear equations $f(x)=0$. Every unknown $x_i$ is bounded between $l_i$ and $u_i$, i.e., $l_i<...
1
vote
1answer
156 views
Eigenvalue problem constrained with a penalty method
I am trying to constrain an eigenvalue problem. I am aware of the method utilizing the nullspace of the constraint vectors but I was wondering if it would be to use a penalty method for the same ...
2
votes
4answers
1k views
Simple methods for solving 2D steady incompressible flow?
I'm trying to make a CFD model where I can place a source and a sink anywhere in a grid and get the fluid flow rate across each cell boundary between those locations. I'm starting simple with a 3x3 ...
0
votes
1answer
829 views
Solve integral equation for unknown constant
Consider the equations
$$\int_0^L \mathbf W(\mathbf u, s) \, \mathrm ds = \mathbf 0$$
where $0 \leq s \leq L$ and $\mathbf u$ is a vector of constants.
Numerically, what is the best way to ...
0
votes
1answer
375 views
FEM, Direct Stiffness Method with a nonlinear displacement constraint in one node
i have a question about a FE problem im working on.
I made a finite element model of an linear elastic block of material (double striped block) attached with a rigid connection to the environment (...
5
votes
1answer
77 views
Projection on Stiefel manifold after integration step
A few days ago, I asked how constraints like $A^T A = I$ can be implemented if one wishes to integrate differential equations of the form $\dot{A}=f(A,t)$. Kirill was so kind to point out that a ...
8
votes
2answers
3k views
Markov (Chain) image generators?
Markov Chains can be used to generate, or auto-complete, text.
https://en.wikipedia.org/wiki/Markov_chain#Markov_text_generators
Training text is read, and some information about the text is ...
3
votes
1answer
150 views
Integration of differential equation with orthogonality constraint
Lets say I have a system of differential equations which has the form
$$\dot{C}_{\alpha,\beta,m} = f_{\alpha,\beta,m}(C_{\alpha,\beta,1},\ldots,C_{\alpha,\beta,N};t).$$
The $f$s are some functions of ...
5
votes
2answers
390 views
Prescribe solution of a PDE at specific points
I am using MATLAB's PDE toolbox to solve the differential equation
$-\nabla\cdot\left(c(x)\nabla u(x)\right) + a(x)u(x) = f(x)$
The particular problem in question is an electrostatic problem, but ...
1
vote
0answers
189 views
Maxwellian distribution of velocities with Shake algorithm present
I am writing a code to perform hybrid monte carlo molecular dynamics. To do this, I need to have a code to initialize the velocities of all particles according to a maxwell distribution. The code is ...
1
vote
1answer
256 views
Minimization constraints without using Lagrange Multiplier
Currently, I am working on an unconstrained energy minimization function, but I need to add some constraints. My system is a 2D lattice with a force applied to it, and I want the sides to be able to ...
1
vote
0answers
51 views
Numerical Implementation of "integrates to some values" type constraint in convex solvers?
I am maximizing a linear functional subject to an integrates to one constraint. More explicitly, my problem is
$$\begin{align}
&\max_{x \in \mathbb{R}^n}\quad c \cdot x\\
&\text{subject to} \...
1
vote
1answer
1k views
Convex Polygon Intersection
Determining the intersection of two convex polygons is one of the fundamental problems in computational geometry .
I'm asking for an algorithm having:
INPUT:
Given two convex polygons P and Q in 2D (...
3
votes
2answers
129 views
How does constraint resolution affect the stability/accuracy of numerical integration?
I understand some basic analysis techniques (local truncation error, global error, zero-stable, absolute stable, etc.) of numerical integration.
But I find it hard to apply these techniques in ...
4
votes
1answer
436 views
Transform from constrained to unconstrained optimization
In a constrained optimization problem, I found in a paper a way to define new variables such that the constraints disappear. They only give the new variable definitions, and I would like to understand ...
2
votes
0answers
81 views
About Convex Geometry
A consistency notion in constraint programming:
Let $P = (X, D, C)$ be a CSP.
Given a set of variables $Y \subseteq X$ with $|Y| = k -1$, a locally consistent instantiation $I$ on $Y$ is $k$-...
3
votes
1answer
1k views
solving a linearly-constrained sparse linear least-squares problem
[ question reposted from https://math.stackexchange.com/questions/786612/solving-a-linearly-constrained-sparse-linear-least-squares-problem ]
Given the system of equations
$Ax=b$, subject to $Cx\le ...
2
votes
2answers
164 views
How to impose a constant constraint PDE
What is the best way to impose a "constant constraint" for a PDE? Specifically, I want to solve an eigenvalue problem $Au=\lambda u$ on the rectangle $(0,2\pi)\times(-\pi/2,\pi/2)$ with periodicity ...
3
votes
1answer
123 views
What's the best way to handle a quadratic constraint
What is the best way to handle a constraint of the type $ax_1^2+x_2^2+...+x_n^2=c$ in a gradient descent algorithm?
I would like to solve an optimization problem of the type:
$$ \min J(x_1,..,x_n)$$ ...
3
votes
0answers
371 views
How much better a bounded BFGS is compared to augmented Lagrangian method with BFGS?
I mean, in handling boxed constraints?
In terms of stability, and more importantly, the numerical performance?
I have already written some well-optimized and well-tested C/CUDA/C++ codes for ...
3
votes
1answer
689 views
BFGS methods for constrained elasticity problems
My dear community,
I am wondering why BFGS methods are not so widely used for simulating mechanical problems which heavily still relies on inverting the hessian matrix. I am essentially interested ...
2
votes
2answers
1k views
Quadratic program With Linear Constraint vs. Eigen Decomposition Time Complexity-Comparison. Which is faster?
Say I had the choice of choosing one out of the following two optimization problems which I could use to solve my problem. Which choice is the fastest? How much of a trade-off would it be-as in - Is ...
8
votes
2answers
5k views
How to get all intersections between two simple polygons in O(n+k)
Basically the formulation of the problem I'd like to solve is very simple. Given 2 simple polygons (without self-intersections) report all intersecting edge pairs in O(n+k) time, where n - is a total ...
5
votes
2answers
528 views
What does symmetrize mean? (imposing multifreedom constraints to stiffness matrix)
I have a small FEM implementation program. And I want to add imposing multifreedom constraints (MFC) feature to it. The theory of master-slave method is given here (page 10 for general case).
...
5
votes
2answers
427 views
Linear regression with quadratic constraints
What methods are suggested to solve problems of the form $\min || {A} x - y ||_k$, subject to $x^T P x \leq c$, and/or $x^T Q x = d$?
10
votes
4answers
4k views
Nonlinear least squares with box constraints
What are recommended ways of doing nonlinear least squares,
min $\sum err_i(p)^2$,
with box constraints $lo_j <= p_j <= hi_j$ ?
It seems to me (fools rush in) that one could
make the box ...
4
votes
1answer
564 views
What is the probabilistic model behind sudoku grids?
I'm talking about the vanilla sudoku game, with 9x9 grids equally split into 9 regions.
I've tried a few approaches to estimate the probability that a specific number is in a specific location, but I ...