Conditions Definition and 1000 Threads

In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear programming to be optimal, provided that some regularity conditions are satisfied.
Allowing inequality constraints, the KKT approach to nonlinear programming generalizes the method of Lagrange multipliers, which allows only equality constraints. Similar to the Lagrange approach, the constrained maximization (minimization) problem is rewritten as a Lagrange function whose optimal point is a saddle point, i.e. a global maximum (minimum) over the domain of the choice variables and a global minimum (maximum) over the multipliers, which is why the Karush–Kuhn–Tucker theorem is sometimes referred to as the saddle-point theorem.The KKT conditions were originally named after Harold W. Kuhn and Albert W. Tucker, who first published the conditions in 1951. Later scholars discovered that the necessary conditions for this problem had been stated by William Karush in his master's thesis in 1939.

View More On Wikipedia.org
Recent contents Top users
  1. M

    Find r(t): Given Initial Conditions

    Homework Statement Given \vec{}r"(t)= 6i-4cos (2t)j+ 9e3tk, r'\vec{} (0)= 4i +3k and r\vec{}(0)=j+k, find r\vec{}(t). Homework Equations The Attempt at a Solution I will appreciate any ideas how to start this problem. Thank you.
  2. S

    Transmission Lines: Boundary Conditions Meaning

    what do boundary conditions mean wid respect to transmission lines??
  3. Cyrus

    Is Pilot Error to Blame for Icing Condition Accidents?

    Don't fly into known icing conditions. http://d.yimg.com/img.news.yahoo.com/util/anysize/400,http%3A%2F%2Fd.yimg.com%2Fa%2Fp%2Fap%2F20090213%2Fcapt.47ac24e5a3de43cf8e46f8a78db23205.plane_into_home_nydd113.jpg?v=2 Pilot error...
  4. C

    Analytic Geometry Problem - find a line in space meeting some conditions

    Hi all! I've appreciated (and lurked :-) this forum for a while. While waiting to find a question I'm able to answer, it's time for my first post (hopefully the first of many). Here's the problem: I'm trying to teach myself euclidean geometry and a found a tough (for me) question to answer in...
  5. F

    Is T an Isomorphism of F^2? Finding Necessary Conditions

    Homework Statement Let T be defined on F^2 by (x1,x2)T=(w*x1+y*x2, z*x1+v*x2) where w,y,z,v are some fixed elements in F. (a) Prove that T is a homomorphism of F^2 into itself. (b) Find necessary and sufficient conditions on w,y,z,v so that T is an isomorphism. The Attempt at a Solution I...
  6. N

    Waves in a coaxial cable: Boundary conditions

    Homework Statement Hi all. I have the following expression, which relates the incoming amplitude with the reflected amplitude at a point x = L in a coaxial cable: A_{\text{reflected}} = \frac{R-Z_0}{R+Z_0}A_{\text{incoming}}. Here R is the resistance at the point x = L and Z0 is the...
  7. J

    COMSOL doing periodic boundary conditions in navier stokes

    Please can anyone tell me how to set this up? I know how to do the required settings in the Physics/Period Conditions. However, to fully implement it, I'm also required to choose boundary conditions in the 2D incompressible navier stokes solver (e.g. wall, inlet, outflow, open boundary...
  8. C

    What are the rank conditions for consistency of a linear algebraic system?

    what are the rank conditions for consistency of a linear algebraic system? my proffessor said that the coefficient matrix augmented with the column value matrix must have the same rank as the coefficient matrix for consistency of the system of equations. however does the term rank apply to...
  9. K

    Electric field and boundary conditions

    Homework Statement One half of the region between the plates of a spherical capacitor of inner and outer radii a and b is filled with a linear isotropic dielectric of permittivity \epsilon_1 and the other half has permittivity \epsilon_2, as shown in the figure. If the inner plate has total...
  10. W

    Progressive wave with initial conditions f(x,0)=0, f'(x,0)=g(x)

    Consider a long straight string that is given an initial impulse. The transverse displacement of the string y(x,t) satisfies the initial condition: y(x,0) = 0 and y'(x,0) = G(x) Show that the solution to the wave eq'n satisfying the intitial condition is y(x,t) = 1/2v[H(x+vt)-H(x-vt)]...
  11. C

    Hydrogen Atom Wavefunction Boundary conditions

    Hi, I have been given a differential equation to use in order to solve for the Hydrogen wavefunction in the ground state using Euler's method. d^2u_nl/dr^2 -(l(l+1)/r^2)*u_nl + 2k*(E_nl-V(r))*u_nl = 0 V(r) = -a/r where a = 1/137.04 I have been given initial conditions u_nl(0) = 0 an...
  12. I

    Conditions on complex plane wave solutions to Maxwell's Equations

    Homework Statement What conditions need to be imposed on \vec{E}0, \vec{B}0, \vec{k} and ω to ensure the following equations solve Maxwell's equations in a region with permittivity ε and permeability µ, where the charge density and the current density vanish: \vec{E} = Re{ \vec{E}0...
  13. S

    Applying Boundary Conditions for the Heat Conduction Equation

    Homework Statement Solve \left(\frac{\partial^{2}}{\partial z^{2}}- \frac{1}{\kappa} \frac{\partial}{\partial t}\right) T=0 with boundary conditions (i) T(0,t)=T_{0}+T_{1} Sin[\omega t] (ii) T is finite as z\rightarrow\inftyHomework Equations Separation of Variables gives: T =...
  14. N

    How do i deal with integral boundary conditions?

    I am trying to solve an ode of the form u"(x)=a(x) where a(x) is some known function and the domain is from -inf to +inf. I am required to use Green's function. The boundary condition is u(0) = Integral[u(x),{x,0,1}] = 0 My Green's function has the form G(x,y) = A(y)*x+B(y) x<y G(x,y)...
  15. D

    Find unit vetors satisfying qualifying conditions HELP test tomorrow

    Find unit vetors satisfying qualifying conditions! HELP test tomorrow Homework Statement Find the unit vectors satisfying qualifying conditions: a. oppositely directed to 3i-4j b. same direction as 2i-j-2k c. same direction as vector from A(-3,2) to B(1,-1) Thoughts. Ok...
  16. T

    Solve Laplace equation with boundary conditions

    Homework Statement Calculate potential function and the electric field for the region between two concentric cylinders, where V ( inner cylinder) = 0 at r = 0.015 m and V(outer cylinder) = 100 for r = 0.025 Homework Equations \Delta (square ) V = 0 The Attempt at a Solution so...
  17. G

    [Q]One question about Magnetic boundary conditions.

    Hi. You know that B_{1n} = B_{2n} as one of the boundary condition when magnetic field is go across from material 1 to material 2, n means direction perpendicular to the boundary surface. I wander this theorem is right in non-uniform field which is function of space variable r...
  18. C

    Calculating the vol. of hydrogen needed to hydrogenate under certain conditions

    Homework Statement Calculate the volume of H2 required to completely hydrogenate 50 grams of glycerol trioleate at 1 atm pressure and 25 degrees Celcius. The ideal gas constant is 0.082. Homework Equations I am unsure if I need the Ideal Gas Equation or not. I know that the ideal gas...
  19. M

    Zero Initial Conditions: Short Circuit & Open Circuit?

    Hi all, a quick question, if we assume zero inital condtions does that mean that we replace each voltage source by a short circuit and a current source with an open circuit??
  20. F

    Understanding Boundary Conditions for Electric Fields

    Hello everyone, if an electric field in a medium with permittivity eps_1 moves at an angle into a material with eps_2, there is refraction. The field in the second medium changes angle. we can see that the tangential component is not changed but the one normal to the surface of separation...
  21. O

    Question related to fill in boundary conditions in comsol

    Firstly I really feel so lucky to find this forum. Since I don't have a strong physics background but now dealing with many problems directly related to physics. I'm now doing some simulation in comsol and need to solve some PDEs. I'm using this PDE coefficient form in comsol. The equations...
  22. S

    # Solving the Unknown Tension using Equilibrium Conditions

    http://www.lasalle.edu/~longo/PHY105/labs/lab4Statics/pulleys3.gif # The tension along the string between knots A and B is unknown. There are four distinct equilibrium conditions, each of which should allow you to calculate the magnitude of the unknown tension 1. the x components for the...
  23. N

    Diff. eq. and boundary conditions

    Homework Statement Hi all. I am given the following differential equation: X'' - k*X=0. I am told that k = -m^2, so the general solution is given by: X = a*cos(m*x)+b*sin(m*x), where a and b are constants. I am also given boundary conditions: 1) X(-Pi) = X(Pi) 2) X'(-Pi) =...
  24. K

    Necessary and sufficient conditions: Fourier Transform

    I don’t know if the question belongs to engineering or math but here it goes. I was taught that a sufficient (not necessary) condition for existence of Fourier transform of f(t) is f(t) is absolutely integratble. I was wondering what are the “necessary and sufficient conditions” for FT of f(t)...
  25. N

    Laplace's equation on a rectangle with mixed boundary conditions

    Homework Statement Solve Laplace's equation inside the rectangle 0 \le x \le L, 0 \le y \le H with the following boundary conditions u(0,y) = g(y)\text{, } u(L,y) = 0\text{, } u_y(x,0) = 0\text{, and } u(x,H) = 0 Homework Equations The Attempt at a Solution I know that with...
  26. D

    Free Electron Model: Why periodic boundary conditions and what is L ?

    Free Electron Model: Why periodic boundary conditions and what is "L"? Right, hello! The quantum free electron model for electrons in solids (in One dimension) says we need to use periodic boundary conditions such that if Y(x) is the wavefunction, then Y(x) = Y(x+L). Where L seems to be...
  27. P

    Solving Euler Equation for F(K) and U(C) with Initial and Terminal Conditions

    The functions K maps to f(K) and C maps to U(C) are given as: F(K) = aK and U(C) = -C^2 +b here a and b are positive constants. the initial and teriminal conditions with the triminal time T = 1/a are K(0) = K_0 and K_T = K(1/a) here K_0 and K_T are positive constants. Write Euler...
  28. S

    Unbelievable Medical Conditions

    A strange list, but this looks like bull**** http://www.oddee.com/item_96473.aspx
  29. W

    Finding a Function of X to Satisfy Certain Conditions

    This should be a dead simple answer, but I don't know what this is called, or what to search on... I need a function of x such that: 0 <= x <= 1 Where f(0) = 0, and f(1) = infinity. I also need the curve to be relatively flat for "lower numbers", say up to 0.3, and begin a very sharp...
  30. N

    Boundary Conditions, Continuum Mechanics

    Mods: I wasn't sure if I should put this here or in DE's, if you think it would be better there, feel free to move it. Everyone: If I have a bunch of particles, which I'm modelling as a continuum, and I want to put periodic boundary conditions which reflect (completely specular reflection)...
  31. R

    Green Function and Boundary Conditions

    Hey folks, I'm trying to find the Green function for the equation -\partial_\mu \partial^\mu \phi = K where K is some source term. Its a 2D problem with the wave confined to a rectangular cavity where the cavity is located at z = 0 and z=a. This tells me that G|_0= G|_a=0 I've pretty...
  32. S

    Exploring the Conditions for Group Closure in Infinite Sets

    Let G be a finite nonempty set with an operation * such that: 1. G is closed under *. 2. * is associative. 3. Given with a*b=a*c, then b=c 4. Given with b*a=c*a, then b=c Give an example to show that under the conditions above, G is no longer a group if G is an infinite set?
  33. T

    How Can I Introduce the Effect of the Magnetic Field Inside the Channel?

    Hi there, I am solving laplace equation in a code i made in C. I am using Finite Difference Method in order to simulate the current pattern. I used the stream function to do that...
  34. S

    Solving ODE: y = $\sqrt {x\ln (x)}$ w/ Initial Conditions

    Homework Statement given this ODE with initial conditions y(1)=0 \[ (x + y^2 )dx - 2xydy = 0 \] Homework Equations solving this ODE gives us \[y = \sqrt {x\ln (x)} \] as we can see this equation is true only for x>=1 in order to use the theorem on existence and uniqueness we isulate...
  35. H

    Circular Plate w/ Hole: Boundary Conditions

    Hey people can u please tell me what will be the boundary conditions for a circular plate with a central hole clamped at the circumference... Plate is axis symmetric and is under uniform load..
  36. E

    Boundary conditions for fluid flow

    What are the general boundary conditions for nonviscous, incompressible fluid flow? I am trying to find the velocity of fluid at the surface of a sphere with the incident fluid having uniform velocity. I am surprised to find in the solution that the radial velocity at the surface does not...
  37. T

    Under what conditions does a function have a power series representation?

    Under what conditions does a function have a power series representation? I am looking for a theorem that says if a function satisfies these conditions then it has a power series representation. Or does all functions have a power series representation?
  38. O

    Hamiltonian & Degeneracy: Conditions

    Hi all, could someone give me a quick answer on the exact conditions for the hamiltonian to be non degenerate, i.e. to have different eigenvalues? thanks in advance.
  39. N

    Born-Von Karman boundary conditions

    I can't understand this conditions, and in general every boundary conditions for problems like this. they states "the choice of boundary conditions can be determined by mathematical convenience (!?) ... for if the metal is sufficiently large, we should expect its bulk properties not to be...
  40. S

    Set these boundary conditions in COMSOL 3.4?

    Hello friends, Thanks in advance for your answers, I am using genreal form of PDE to solve system of PDEs. I am dealing with cyllindrical co-ordinates under axisymmetric case. I am not able to understand how to implement boundary conditions such as, DEL. Gamma=F is system of PDEs where...
  41. I

    Atomic Isolation: Conditions for Line Spectra

    Hi Guys! *waves* Anyway, I was just wondering what conditions and in what state are atoms sufficiently isolated so that it gives rise to a line spectra. I thank you all for any help you provide in advance. Many thanks, Icetray
  42. C

    Boundary conditions on magnetostatic

    Hi I'm trying to solve a magnetostatic problem and I'm not sure which boundary conditions must be applied to the magnetic vector potential (A) on magnetostatic problems? Thanks in advance.
  43. S

    Solving the Diffusion Equation with Boundary Conditions

    Hey all, I'm wondering if someone can help me understand how to apply the boundary conditions to the diffusion equation in one dimension. Diffusion equation is: \frac{\partial u}{\partial t}=D*\frac{(\partial)^{2}u}{\partial x^{2}} The initial condition is: u(x,0)=0 And the boundary...
  44. D

    This could be the solution to your confusion.

    Hello hello, I cannot for the life of me wrap my head around the idea of a boundary condition. I understand the idea (at least I think I do) of solving a differential equation with given initial conditions. But is solving for a magnetic field or electric field while enforcing...
  45. V

    Formation of elements under conditions of thermodynamic equilbrium

    [Sorry about the long post] I'm doing an essay where I am exploring whether or not elements were, for the most part, formed under conditions of thermodynamic equilibrium. We know that some element clearly aren't (such as Potassium 40 and uranium which decay radioactivly). I've scoured the web...
  46. M

    Are acoustic wave reflection and the boundary conditions truly interdependent?

    I am studying acoustic wave reflection. The boundary conditions of acoustics are continuity of pressure and normal particle velocity. Can anyone tell me if these boundary conditions are completely independent? (Since the pressure and particle velocity are in phase, I would believe they are not...
  47. A

    Conditions for quantised or continuous energies

    Homework Statement For a particle moving in a potential V(x), what are plausible forms of V(x) that give: (i) entirely continuous, (ii)entirely quantised (iii) both continuous and quantised energies of the particle? Sketch, with justification, the forms of V(x) for each of...
  48. F

    Differential equation with singular boundary conditions

    Hey guys, just need some hints with this doosey Homework Statement We have (x^2 y')' + ax^2y = 0 where a the eigenvalue (a sturm-lioville problem) (sp?) with y'(0)=y(1) = 0 and we get the hint to substitute f = y/x. The Attempt at a Solution Ok so i get the general solution being a sum of...
  49. P

    Alkyl Halide Mechanism: E1 vs. E2 in Acidic and Basic Conditions

    This is my question... For the alkyl halide tell which mechanism, E1 or E2, will predominate under both stongly basic (with large base) conditions and strongly acidic. Tell if each reaction is expected to proceed relatively quickly, moderately, or slow (based on sterics for E2 and carbocation...
  50. A

    Momentum eigenfunctions with periodic boundary conditions

    Homework Statement A particle of mass m is confined to move in one dimension. its wavefunction is periodic with period L\gg 1 - i.e. periodic boundary conditions are imposed. a)Determine the eigenfunctions and eigenvalues of momentum. Normalise the eigenfunctions on the interval [0,L)...
Back
Top