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.
51
questions
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44
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Over-specification of conjugate heat transfer coupling conditions
I am trying to implement steady state conjugate heat transfer using a monolithically coupled scheme. In this simulation, the computational domain is divided into fluid and solid subdomains. Over time, ...
- 63
2
votes
1
answer
53
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Solving constrained odes's using inbuilt solvers in Matlab/Octave
I would like to solve a set of coupled second order differential equations using inbuilt Matlab/Octave subroutines. These equations arise when trying to model sliding of mass ($m_2$) over a wedge of ...
5
votes
1
answer
55
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What are the various methods in adding an additional constraint to the quadratic spline interpolation problem
I am taking a class on numerical analysis. While the professor was deriving the theory behind quadratic splines, the professor mentioned that a quadratic spline function has the form:
$$
p_{i}(x)=a_{i}...
- 151
1
vote
0
answers
60
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SLSQP solver scipy with linear subset constraints
I have been trying to solve a least squares problem of the following form:
$$
\begin{equation}
\min_{\vec{x}} \frac{1}{2} \lVert f(\vec{x}) - f_{\text{target}} \rVert_{2}^2 + \alpha\Big( \frac{1-\rho}{...
- 11
2
votes
0
answers
59
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How "kinematic" rigid bodies are implemented in physics engines
In most physics engines there's this concept of "static" bodies, which act as rigid bodies with infinite mass. Then there are "kinematic" bodies that act as static bodies, but ...
- 143
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0
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44
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The condtion for Augmented Langrangian Multiplier
I am currently learning the usage of Augmented Lagrangian Multiplier to achieve my equality constraint. I have learnt from the https://en.wikipedia.org/wiki/Augmented_Lagrangian_method that I have two ...
3
votes
0
answers
135
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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 ...
- 181
2
votes
0
answers
33
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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 ...
- 201
1
vote
1
answer
308
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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}...
- 141
2
votes
1
answer
782
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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....
- 35
1
vote
1
answer
77
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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 ...
- 13
3
votes
1
answer
840
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 ...
- 459
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0
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109
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 ...
- 2,346
1
vote
1
answer
893
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)?
...
- 13
-1
votes
1
answer
26
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
0
answers
499
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, ...
- 143
2
votes
0
answers
32
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}...
- 223
2
votes
1
answer
150
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:
...
- 23
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votes
1
answer
1k
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Defining a soft constraint in cvxpy
I am using cvxpy to do a simple portfolio optimization.
I implemented the following dummy code
...
- 111
1
vote
2
answers
131
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 ...
- 111
3
votes
1
answer
853
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 ...
- 1,300
6
votes
1
answer
1k
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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 ...
- 161
1
vote
1
answer
680
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 ...
- 11
1
vote
0
answers
290
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 ...
- 321
6
votes
1
answer
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<...
- 439
1
vote
1
answer
182
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 ...
- 121
2
votes
4
answers
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 ...
- 21
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votes
1
answer
849
views
Solve integral equation for unknown constant
Consider the equations
$$\int_0^L \mathbf W(\mathbf u, s) \, \mathrm ds = \mathbf 0$$
where $0 \leq s \leq L$ and $\mathbf u$ is a vector of constants.
Numerically, what is the best way to ...
- 187
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votes
1
answer
408
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FEM, Direct Stiffness Method with a nonlinear displacement constraint in one node
i have a question about a FE problem im working on.
I made a finite element model of an linear elastic block of material (double striped block) attached with a rigid connection to the environment (...
- 13
5
votes
1
answer
102
views
Projection on Stiefel manifold after integration step
A few days ago, I asked how constraints like $A^T A = I$ can be implemented if one wishes to integrate differential equations of the form $\dot{A}=f(A,t)$. Kirill was so kind to point out that a ...
- 277
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votes
2
answers
3k
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Markov (Chain) image generators?
Markov Chains can be used to generate, or auto-complete, text.
https://en.wikipedia.org/wiki/Markov_chain#Markov_text_generators
Training text is read, and some information about the text is ...
- 193
3
votes
1
answer
178
views
Integration of differential equation with orthogonality constraint
Lets say I have a system of differential equations which has the form
$$\dot{C}_{\alpha,\beta,m} = f_{\alpha,\beta,m}(C_{\alpha,\beta,1},\ldots,C_{\alpha,\beta,N};t).$$
The $f$s are some functions of ...
- 277
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votes
2
answers
424
views
Prescribe solution of a PDE at specific points
I am using MATLAB's PDE toolbox to solve the differential equation
$-\nabla\cdot\left(c(x)\nabla u(x)\right) + a(x)u(x) = f(x)$
The particular problem in question is an electrostatic problem, but ...
- 83
1
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0
answers
195
views
Maxwellian distribution of velocities with Shake algorithm present
I am writing a code to perform hybrid monte carlo molecular dynamics. To do this, I need to have a code to initialize the velocities of all particles according to a maxwell distribution. The code is ...
- 291
1
vote
1
answer
364
views
Minimization constraints without using Lagrange Multiplier
Currently, I am working on an unconstrained energy minimization function, but I need to add some constraints. My system is a 2D lattice with a force applied to it, and I want the sides to be able to ...
1
vote
0
answers
52
views
Numerical Implementation of "integrates to some values" type constraint in convex solvers?
I am maximizing a linear functional subject to an integrates to one constraint. More explicitly, my problem is
$$\begin{align}
&\max_{x \in \mathbb{R}^n}\quad c \cdot x\\
&\text{subject to} \...
- 466
1
vote
1
answer
1k
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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 (...
- 41
3
votes
2
answers
133
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 ...
- 327
4
votes
1
answer
461
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 ...
- 41
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0
answers
81
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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 $k$-...
- 41
4
votes
1
answer
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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 ...
- 43
2
votes
2
answers
181
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 ...
- 965
3
votes
1
answer
133
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:
$$ \min J(x_1,..,x_n)$$ ...
- 965
3
votes
0
answers
380
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 ...
- 331
3
votes
1
answer
709
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 ...
- 41
2
votes
2
answers
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 ...
- 269
8
votes
2
answers
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
2
answers
546
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).
...
- 501
5
votes
2
answers
449
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 $x^T Q x = d$?
- 333
10
votes
4
answers
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 ...
- 892