What is Constraints: Definition and 216 Discussions

The theory of constraints (TOC) is a management paradigm that views any manageable system as being limited in achieving more of its goals by a very small number of constraints. There is always at least one constraint, and TOC uses a focusing process to identify the constraint and restructure the rest of the organization around it. TOC adopts the common idiom "a chain is no stronger than its weakest link". This means that processes, organizations, etc., are vulnerable because the weakest person or part can always damage or break them or at least adversely affect the outcome.

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  1. gfd43tg

    Minimizing with constraints and linear function

    Hello, I am going over these slides and I am very confused on a couple parts. First of all on the first slide, I don't understand why a linear function has the form ##f(x) = c^Tx##. How is that equal to ##c_{1}x_{1} + c_{2}x_{2} + \dots + c_{n}x_{n}##. Wouldn't this depend on how you define...
  2. ChrisVer

    Constraints on Chiral superfield

    Suppose we have a superfield \Phi(x,\theta,\bar{\theta}) this can be expanded in component fields in the standard way as: \Phi(x,\theta,\bar{\theta})= c(x) + \theta \psi(x) + \bar{\theta} \bar{ζ}(x) + \theta^{2} F(x) + \bar{\theta}^{2} Z(x) + \theta \sigma^{\mu} \bar{\theta} u_{\mu}(x) +...
  3. gfd43tg

    Optimization with constraints matlab

    Homework Statement Just a heads up, this is a problem with parts (a) - (o). I am working on (k). I am working on problem 5 in the attached PDF. I will show my code for the other parts. We were told to use N = 5 while writing the code for debugging and testing, but run N = 500 for the real...
  4. A

    Lagrange Multipliers with Multiple Constraints?

    Homework Statement Using Lagrange multipliers, find the max and the min values of f: f(x,y,z) = x^2 +2y^2+3x^2 Constraints: x + y + z =1 x - y + 2z = 2Homework Equations ∇f(x) = λ∇g(x) + μ∇h(x)The Attempt at a Solution Using Lagrange multipliers, I obtained the equations: 2x = λ + μ 4y =...
  5. A

    How can I properly constrain a 3D truss beam in ANSYS using only beam elements?

    Hello! I'm trying to model my truss with FEM using only beam elements in ANSYS, but I am experiencing difficulties with the constraints between the members (or coupling of the DOFs). For instance, I want my truss chords to be continuous and my lattice members to be pinned to them. I couple...
  6. D

    Post-optimality analysis: Change in one of the constraints

    Homework Statement Consider the LP: max \, -3x_1-x_2 \,\,s.t. \,\,\,\, 2x_1+x_2 \leq 3 \quad \quad \ -x_1+x_2 \geq 1 \quad \quad \quad \quad \ x_1,x_2 \geq 0Suppose I have solved the above problem for the optimal solution. (I used dual simplex and get (0,1) as the optimal solution.) Now...
  7. phoenixXL

    Velocity - String(Pulley) constraints

    Homework Statement A bead C can move freely on a horizontal rod. The bead is connected by blocks B and D by a string as shown in the figure. If the velocity of B is v. Find the velocity of block D. Homework Equations As the string is inextensible the velocity of the string along the...
  8. A

    Is it possible to prove this set inequality given the constraints?

    Homework Statement Homework Equations I have to use these set identities: The Attempt at a Solution Pretty sure this is impossible since it's an inequality.
  9. A

    Optimization with schedule constraints

    Hi, I have a optimization problem and I need to find a way to solve it even if only with an approximate solution. Let's suppose we have a finite set of vertical containers each with a distinct liquid chemical inside.(say a handful of vertical pipes). At the top, these containers have an...
  10. R

    Help with shared constraints (game theory)

    I've been struggling with shared constraints problems for a while now. I have a game between two players with a shared constraint. For example, player 1 is trying to maximize f(x,y) by choosing x, and player 2 is trying to maximize g(x,y) by choosing y. The players are competing in a...
  11. B

    Non-holonomic constraints in field theory

    My question is the following: In field theory, if I have a constraint \chi(q_a, p_a, \partial_i q_a) that depends on the generalised coordinates q_a, momenta p_a and spatial derivatives only of the q_a \partial_i q_a does this count as a non-holonomic constraint? Or is it only...
  12. anemone

    MHB Optimization With Two Constraints

    Hi MHB, I've come across this problem recently: If a²+b²=2 and (c-3)²+(d-4)²=1, find the maximum value of ad-bc. I haven't solved it and actually, I don't know of any algebraic method I could use to solve it and I am wondering if this problem is doable with the Lagrange Multiplier...
  13. B

    Primary constraints for Hamiltonian field theories

    I am currently trying to carry out the construction of the generalised Hamiltonian, constraints and constraint algebra, etc for a particular field theory following the procedure in Dirac's "Lectures on quantum mechanics". My question is the following: I have momentum variables that depend on the...
  14. M

    Constraints and Static Determinacy

    Hello, Is it possible for a structure to be completely constrained and statically indeterminate, or partially constrained and statically determinate? Or does one come with the other automatically? I am having difficulties determining if a structure is partially constrained or completely...
  15. G

    Find a 2-arguments function from six constraints on its derivatives

    Hello, I need to find a two-arguments function u(x,y) which satisfies six constraints on its derivatives. x and y are quantities so always positive. 1&2: On the first derivatives: du/dx>0 for all x & du/dy>0 for all y (so u is increasing in x and y) 3&4: On the second derivatives...
  16. inflector

    Paper: Constraints on Dark Matter in the Solar System

    Any comments on the recent N. P. Pitjev and E. V. Pitjeva paper: Constraints on Dark Matter in the Solar System arXiv: http://arxiv.org/abs/1306.5534 MIT Technology Review article...
  17. C

    Linear subspace constraints and notation.

    Homework Statement The original printed problems can be found as attachments. The questions ask if a set S is a subset Rn. Give Reasons Question 1.) S is the set of all vectors [x1,x2] such that x12 + x22 < 36Question 2.) S is the set of all vectors [x1,x2,x3] such that: x2= 2x1 x3 = 3x1...
  18. S

    Constraints on possible fifth fundamental force

    Anyone read the article on this? http://phys.org/news/2013-06-precise-quantum-electrodynamics-constrain-fundamental.html I made an effort to read to arXiv paper, but I'm still working on my understanding of QFT, so I didn't get too much out of it.
  19. K

    Constraints on Acceleration Given Endpoints of Motion

    Homework Statement A particle of mass M moves on the X-axis as follows: It starts from rest at t = 0 from the point x = 0 and comes to rest at t = 1 at the point x = 1. No other information is available about it smotion at intermediate times (0 < t < 1). If α denotes the instantaneous...
  20. N

    Metric constraints in choosing coordinates

    Hello all, I've been puzzled by this problem for some time now and was wondering if anyone here could help me out. Textbooks on GR (specifically when going into gravitational waves) tend not to elucidate this. It's often taken for granted that through the gauge diffeomorphism invariance (or...
  21. bcrowell

    19th-century constraints on properties of the aether

    Did physicists ever try to put empirical constraints on the properties of the aether? I recall reading a popularization by Isaac Asimov in which he remarked that the aether would have had to have a very low density, and then to explain the high speed of light it would have had to have a...
  22. U

    MHB Calculus of variations with integral constraints

    http://img835.imageshack.us/img835/2079/minimise.jpg Both p(x,y) and q(x,y) are probability density functions, q(x,y) is an already known density function, my job is to minimise C[p,q] with respect to 3 conditions, they are listed in the red numbers, 1, 2, 3. Setting up the lagrange function...
  23. L

    Angular constraints on the Inverted Double Pendulum - 'Acrobot'

    I am attempting to recreate Sutton's work on the 'Acrobot' and have modeled a good solution to the following: http://webdocs.cs.uAlberta.ca/~sutton/book/ebook/node110.html The physics is implemented in exactly the same way, however my particular Java implementation requires some constraint...
  24. M

    Maxwell's Equations in Vacuum: Constraints on Wave

    Homework Statement Condensed/simplified problem statement \vec{E} = f_{y}(x-ct)\hat{y} + f_{z}(x-ct)\hat{z} \\ \vec{B} = g_{y}(x-ct)\hat{y} + g_{z}(x-ct)\hat{z} \\ All the f and g functions go to zero as their parameters go to ±∞. Show that gy = fz and gz = -fy Homework Equations \nabla...
  25. Astrum

    What is the Significance of Constraints in Relationships Between Variables?

    I have no idea what constraints are, nor do I understand why they are important. I get where the constraints in these two examples come from, but not why they're significant. These seem to be relationships between variables, and not much of a "constraint" in the sense I know the word...
  26. F

    Normal force max min constraints on a roller coaster

    Homework Statement passengers cannot have a normal force equal to 0 or greater than 4 times their weight. What are the heights H1 and H2. Coaster starts at H1 and and ends at H2. H1>H2 and there is a low point between the two hills defined as zero height. The radius of the curve at the...
  27. M

    Bead on a Rotating Hoop - Constraints (Holonomic / Nonholonomic)

    1. Homework Statement We have a bead sliding with friction on a hoop oriented vertically. First the hoop rotates about its center with rotation axis perpendicular to its plane. Second, the hoop rotates about a vertical axis as well. In both of these cases, are the constraints holonomic or...
  28. D

    Fortran Fortran: Creating a sequence with constraints

    I'm trying to write a program in fortran that will create a sequence of numbers (starting with a number that I input) that follow the following constraints: If the number (n) in the sequence is even, then the next number in the sequence will be n/2. If the number (n) in the sequence is odd, then...
  29. A

    Constraints on the Gibbs Equation, Tds = dh - vdP

    Homework Statement What constraints are imposed on the use of the Gibbs equation Tds = dh - vdP Homework Equations Tds = dh - vdP The Attempt at a Solution I seem to be stuck on this question. So far I have come up with the following constraints, but I'm not even sure if they are...
  30. J

    Constraints on matrix-variate normal distributions

    Hello, all. I'm wondering about matrix-variate normal distributions. I know they normally assume an n x p random matrix, X, and associated row and column covariance matrices Omega and Sigma, but I'm wondering how the probability density function changes if X is comprised of a square...
  31. J

    Constraints, Concept , Kant & Space

    In a recent thread, language was described as an activity where: a set of rules is used to define constrains on the world. For instance the word car limits they type of objects in the world which are likely to be denoted by the word car because one might not normally expect one to call a house...
  32. M

    ANSYS Static Structural boundary constraints issues

    Hey all, First off, I'd like to mention that I am completely unfamiliar with this ANSYS and have been fighting with this program for last 2 and half weeks. Any feedback and help is greatly appreciated! Please refer to the photos attached for referral. My project currently involves analyzing...
  33. T

    Fist and second order constraints in a system?

    I've tried with Goldstein but no luck, i need to understand how the constraint, especially the second class act on system, i also referred Dirac's lecture, they were quiet good, but if u can suggest some books which can help me learn first and second class constraints with examples and problems...
  34. F

    Multidimensional Gaussian integral with constraints

    Homework Statement The larger context is that I'm looking at the scenario of fitting a polynomial to points with Gaussian errors using chi squared minimization. The point of this is to describe the likelihood of measuring a given parameter set from the fit. I'm taking N equally spaced x values...
  35. Peeter

    Dealing with conflicting no-slip Navier-Stokes boundary value constraints?

    The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces. So, for example, in a shearing flow where there is a moving surface, the fluid velocity at the fluid/surface interface has to...
  36. N

    How do you set up this lp problem? I'm not sure how to set up the constraints.

    A company produces three products A1, A2, A3 by mixing three ingredients B1, B2, B3. The selling price for A1, A2 and A3 is $13, 14 and 16 $/kg, respec- tively, and at most 75,80 and 90 kg of each can be sold daily. The cost of B1,B2,B3 is 7, 2 and 4 $/kg and the daily supply is at most 40, 95...
  37. K

    How to visualize Constraints in Constrained Optimization Problems?

    That’s an issue for me. I don’t know how should I visualize constraints in constrained optimization problems in R^{3}. This is a problem cause I cannot see how it works the multiplier solution in the inequality constraints. That’s not a matter of exercises, that’s really a problem of...
  38. bcrowell

    Constraints on interactions of tachyons

    Now that the superluminal neutrino fiasco is winding down, I'm interested in seeing if I can consolidate what I know about tachyons. One of the things I learned from following the OPERA debacle is that you can have tachyons without Lorentz violation, or you can have FTL particles (still called...
  39. tom.stoer

    Constraints, measure and vertex amplitude in LQG

    Have a look at http://arxiv.org/abs/1202.5039 Degenerate Plebanski Sector and its Spin Foam Quantization Authors: Sergei Alexandrov (Submitted on 22 Feb 2012) Abstract: We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and...
  40. M

    Least squares estimation with quadratic constraints (M*M = 0)

    Hello there, currently I am trying to solve a least squares problem of the following form: min_{M} ||Y - M*X||^2 where M is a 3x3 matrix and Y and X are 3xN matrices. However, the matrix M is of a special form. It is a rank 1 matrix which satisfies M*M = 0_{3x3} and the trace of M is zero...
  41. E

    Can nonholonomic constraints always be expressed as inequalities?

    So far, every nonholonomic constraint I have seen can be expressed as a collection of inequalities involving the coordinates of the system. For example, a small ball rolling down a sphere with radius a has the constraint r^2-a^2\geq 0, where r is the radial coordinate of the ball. Can every...
  42. A

    Degrees of freedom an constraints

    I'm not quite sure I get the idea of a degree of freedom for a system. First of all: Is there freedom in characterizing the DOF for a system - i.e. will specifying the DOF for a system relative to any coordinate system always be the same? Next let me do an example: If we have 2 particles free...
  43. R

    Constraints for New Fundamental Force

    What are the constraints (is this the right word) for introducing new fundamental force? Can our Standard Model accommodate a fifth one? Or would it mess up the math so badly that the present four fundamental forces is the final limit?
  44. A

    Dot cancellation (holonomic constraints)

    I started to read Analytical Mechanics. It said that if holonomic constraints are defined as: r = r(q1, q2, ... qn, t) (or without time) This equation holds (dot cancellation): ∂r'/∂q_k' = ∂r/∂q_k where ' specified derivatives. And the question was given to check if it works for...
  45. D

    Solving f(x,y,z) with x,y,z Constraints

    Homework Statement f(x,y,z) = e^(2x-z) W: x+y+z ≤ 1, x,y,z ≥ 0 Homework Equations 0 ≤ x ≤ 1-y-z 0 ≤ y ≤ 1-x-z 0 ≤ z ≤ 1-x-y The Attempt at a Solution I tried dzdydx and dydzdx but they don't work... or am I doing something wrong?
  46. A

    Max/min with constraints

    Homework Statement Find max/min of x^2+y^2+z^2 given x^4+y^4+z^4=3Homework Equations Use of gradient vectors related by LaGrange MultiplierThe Attempt at a Solution \begin{gathered} f\left( {x,y,z} \right) = {x^2} + {y^2} + {z^2};g\left( {x,y,z} \right) = {x^4} + {y^4} + {z^4} - 3 = 0 \\...
  47. haushofer

    Primary constraints and Nambu-Goto action

    Hi, I have a fairly simple question, in particular for the Nambu-Goto string, S = - T \int d^2 \sigma \sqrt{-\gamma} where gamma is the induced metric on the worldsheet. The canonical momenta are p_{\mu} = - T\sqrt{-\gamma}\gamma^{a0}\partial_a x_{\mu} From this it is quite straightforward...
  48. Mordred

    Exploring the Time Constraints of Black Hole Mergers

    THe universe is around 14 billion years matter falling into the singularity appear to take infinite time. So how would two black holes have had the time to complete a merger under those conditions? According to my understanding of GR we should be able to see mergers still in progress as the...
  49. M

    Generating multivariate normal vectors under constraints

    Hello all, I wonder if anybody knows of a way of generating a random normal vector (i.e. a variate from a multivariate normal distribituion) in which one or more of the vector's values are fixed?. For example, I may want to choose a random vector from a four-dimensional multivariate normal...
  50. M

    Optimization Solver - BFGS method with bound constraints

    Hello, I am working on a research project that requires me to write a solver for solving a particular problem. I could really use some math advice if anyone is willing to assist. I need to minimize a non-linear objective functions of 5 variables. It is a pretty complex function. Each of the...
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