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.

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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}{...
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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 ...
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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 ...
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3 votes
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102 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 ...
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2 votes
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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 ...
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1 answer
254 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}...
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  • 141
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558 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....
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1 answer
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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 ...
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3 votes
1 answer
747 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 ...
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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 ...
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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)? ...
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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 ...
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2 votes
0 answers
448 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, ...
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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}...
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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: ...
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1 answer
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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 ...
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2 answers
122 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 ...
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3 votes
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756 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 ...
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6 votes
1 answer
950 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 ...
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1 vote
1 answer
652 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 ...
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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 ...
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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<...
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  • 439
1 vote
1 answer
168 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 ...
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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 ...
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1 answer
844 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 ...
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  • 187
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1 answer
392 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 (...
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5 votes
1 answer
89 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 ...
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9 votes
2 answers
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 ...
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3 votes
1 answer
163 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 ...
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5 votes
2 answers
413 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 ...
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1 vote
0 answers
192 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 ...
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1 vote
1 answer
311 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 ...
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1 vote
0 answers
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} \...
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1 vote
1 answer
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 (...
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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 ...
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4 votes
1 answer
449 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 ...
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2 votes
0 answers
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 $k$-...
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4 votes
1 answer
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 ...
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2 votes
2 answers
178 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 ...
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3 votes
1 answer
128 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: $$ \min J(x_1,..,x_n)$$ ...
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3 votes
0 answers
377 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 ...
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3 votes
1 answer
700 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 ...
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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 ...
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  • 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 ...
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5 votes
2 answers
535 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). ...
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  • 501
5 votes
2 answers
443 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 $x^T Q x = d$?
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  • 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 ...
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  • 892
4 votes
1 answer
565 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 ...
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