Newest 'constraints' Questions

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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 ...

asked Jun 10 at 15:17

bobinthebox

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30 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 ...

finite-element constraints conservation

asked Mar 2 at 15:43

TheCodeNovice

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vote

1answer

127 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}...

optimization constrained-optimization convex-optimization constraints

asked Dec 25 '20 at 16:22

ecjb

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vote

1answer

171 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....

ode scipy constraints

asked Oct 30 '20 at 12:13

user606273

252 bronze badges

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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 ...

optimization constrained-optimization constraints

asked Oct 11 '20 at 18:50

Evan Honnold

132 bronze badges

3

votes

1answer

460 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 ...

python constrained-optimization nonlinear-programming constraints gekko

asked Apr 3 '20 at 5:32

Natasha

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votes

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91 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 ...

finite-element constraints weak-solution

asked Mar 18 '19 at 14:47

MPIchael

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1

vote

1answer

583 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)? ...

optimization constrained-optimization constraints

asked Nov 22 '18 at 12:30

os12

133 bronze badges

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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 ...

nonlinear-equations convex-optimization constraints semidefinite-programming

asked Nov 13 '18 at 9:38

Muhammad Usman

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0answers

357 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, ...

finite-element solid-mechanics constraints

asked Jun 20 '18 at 22:44

Huayi Wei

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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}...

convex-optimization constraints

asked May 24 '18 at 16:46

jjjjjj

1936 bronze badges

2

votes

1answer

34 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: ...

nonlinear-programming constraints mixed-integer-programming constrained-optimization

asked May 3 '18 at 15:17

user1372338

232 bronze badges

0

votes

1answer

881 views

Defining a soft constraint in cvxpy

I am using cvxpy to do a simple portfolio optimization. I implemented the following dummy code ...

optimization constrained-optimization constraints cvxpy

asked Mar 30 '18 at 16:24

ThatQuantDude

1112 bronze badges

1

vote

2answers

98 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 ...

convex-optimization constrained-optimization constraints

asked Mar 20 '18 at 20:20

quiet

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3

votes

1answer

557 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 ...

optimization constrained-optimization conjugate-gradient constraints quasi-newton

asked Mar 20 '18 at 12:19

Costis

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6

votes

1answer

649 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 ...

constrained-optimization constraints discrete-optimization

asked Dec 27 '17 at 14:27

user3124074

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vote

1answer

554 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 ...

optimization python constraints

asked Dec 7 '17 at 2:46

Isabella Huang

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vote

0answers

238 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 ...

finite-element numerical-analysis boundary-conditions constraints

asked Nov 14 '17 at 8:03

Wenjin Xing

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6

votes

1answer

1k 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<...

iterative-method newton-method constraints

asked Apr 10 '17 at 17:06

Manu

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vote

1answer

147 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 ...

linear-algebra eigenvalues constraints penalty-method

asked Jan 31 '17 at 10:35

user1941126

1213 bronze badges

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 ...

fluid-dynamics constraints incompressible

asked Jan 13 '17 at 1:25

Calvin

212 bronze badges

0

votes

1answer

774 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 ...

integral-equations constraints

asked Oct 7 '16 at 20:48

namu

18710 bronze badges

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votes

1answer

360 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 (...

finite-element nonlinear-equations constraints stiffness

asked May 23 '16 at 10:42

Jonathan_P

134 bronze badges

5

votes

1answer

70 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 ...

ode constrained-optimization runge-kutta constraints

asked Feb 5 '16 at 20:34

Merlin1896

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7

votes

2answers

2k 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 ...

algorithms iterative-method machine-learning computer-vision constraints

asked Feb 4 '16 at 19:17

alan2here

1736 bronze badges

3

votes

1answer

146 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 ...

ode constrained-optimization runge-kutta constraints

asked Feb 2 '16 at 17:10

Merlin1896

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5

votes

2answers

373 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 ...

matlab finite-element constraints

asked Oct 23 '15 at 15:18

Stuart Barth

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1

vote

0answers

187 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 ...

monte-carlo molecular-dynamics constraints

asked Sep 30 '15 at 20:37

user3225087

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vote

1answer

203 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 ...

constrained-optimization constraints

asked Jun 16 '15 at 15:36

alpha-helix1123

113 bronze badges

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vote

0answers

49 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} \...

optimization convex-optimization constraints

asked May 5 '15 at 17:35

Tom Hallward

1114 bronze badges

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 (...

computational-geometry convex-optimization geometry constraints

asked Dec 29 '14 at 14:25

Limeme90

415 bronze badges

3

votes

2answers

128 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 ...

finite-difference convergence stability time-integration constraints

asked Oct 24 '14 at 2:25

TheBusyTypist

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4

votes

1answer

424 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 ...

constrained-optimization computational-physics constraints

asked Jul 7 '14 at 1:50

J-D

414 bronze badges

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 $k$-...

computational-geometry convex-optimization constrained-optimization combinatorics constraints

asked May 25 '14 at 16:48

Limeme90

415 bronze badges

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 ...

optimization least-squares constraints linear-system

asked May 9 '14 at 10:09

strangelyput

334 bronze badges

2

votes

2answers

161 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 ...

finite-difference boundary-conditions constraints

asked Dec 3 '13 at 22:10

Beni Bogosel

8537 silver badges13 bronze badges

3

votes

1answer

110 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: $$ \min J(x_1,..,x_n)$$ ...

constraints constrained-optimization

asked Sep 4 '13 at 17:53

Beni Bogosel

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3

votes

0answers

361 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 ...

optimization constraints

asked Apr 29 '13 at 23:18

user0002128

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3

votes

1answer

677 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 ...

linear-solver constraints newton-method

asked Apr 18 '13 at 12:24

tom

412 bronze badges

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 ...

optimization complexity convex-optimization constraints quadratic-programming

asked Oct 16 '12 at 18:14

hearse

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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 ...

computational-geometry constraints

asked Apr 24 '12 at 19:03

Sergei Ivanov

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5

votes

2answers

508 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). ...

finite-element constraints block-decomposition

asked Apr 10 '12 at 20:12

danny_23

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5

votes

2answers

393 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 $x^T Q x = d$?

regression constraints

asked Mar 26 '12 at 18:37

Emre

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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 ...

optimization constraints

asked Mar 24 '12 at 16:43

denis

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4

votes

1answer

560 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 ...

combinatorics constraints

asked Jan 18 '12 at 21:59

zneak

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