# What is Conditions: Definition and 1000 Discussions

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
1. ### Calculate this Integral around the Circular Path using Green's Theorem

Is my resolution correct? I can't identify. Calculate the line integral ∮C(2ydx+3xdy), where C is the circle x2+y2=1, using the Green's Theorem. Green's Theorem: Let M and N be functions of two variables x and y, such that they have continuous first partial derivatives in an open disk B in...
2. ### I Optical pumping vs Rabi cycle - what is the difference between their conditions?

Optical pumping "is a process in which light is used to raise (or "pump") electrons from a lower energy level in an atom or molecule to a higher one". In contrast, Rabi cycle "is the cyclic behavior of a two-level quantum system in the presence of an oscillatory driving field." In the first we...
3. ### Is it possible to find matrix A satisfying certain conditions?

Since Ax = b has no solution, this means rank (A) < m. Since ##A^T y=c## has exactly one solution, this means rank (##A^T##) = m Since rank (A) ##\neq## rank (##A^T##) so matrix A can not exist. Is this valid reasoning? Thanks

8. ### A Two degrees of freedom in GR after boundary conditions specified?

I read there are 2 degrees of freedom in GR after boundary conditions specified. Does that mean 2 equations are enough for EFE equivalent? Those two seem like the amplitude and a phase.
9. ### Fortran Need help with Jacobi relaxation method for Dirichlet boundary conditions

program r_jacobi implicit none !!!!Variables!!! real*8 V, V_1, V_2, Lx, Ly integer n ,i , j, k, nx, ny real*8, allocatable :: arrx(:), arry(:), phi(:,:,:) real*8 x, xi, xf, y, yi, yf, dx, dy real*8 d, q, bx, by V=1 V_1=V V_2=-V Lx = 2 Ly = 1 nx = 200 ny = nx/2...
10. ### DC motors and Induction motor: What does "no load conditions" mean?

TL;DR Summary: So I'm just confused when the question asks me to solve for the no load speed of DC motors and induction motors. Does no load condition mean that the output torque (Tout) is zero? This is what I was assuming so far for both DC and induction motor. Is no load condition the same...
11. ### A The boundary conditions in reference to Laplace's equation

We have inhomogenous dirichlet boundary conditions (well understood)....the laplace equation is a steady state equation and we can clearly see that in 2D..it will be defined by 4 boundary conditions and NO initial condition...having said that; kindly have a look at the continuation below... I...
12. ### POTW Sufficient Conditions for a Covering Space

Prove that every surjective local homeomorphism ##\pi : \tilde{X} \to X## from a compact Hausdorff space ##\tilde{X}## to a Hausdorff space ##X## is a covering space.
13. ### A How to solve Diffusion Equation with time dependant conditions?

U=U(x,t) Ut=DUxx; 0<=x<=L, t>0 U(x,0)=0 0<x<=L U(0,t)=a(t); t>0 *a(t) is known function* (dU/dx)=0 for x=L I have looked into many ways but not one is usable for diffusion equation with this boundary conditions.
14. ### Checking assumptions in boundary conditions of double well system

The idea here (as I'm told) is to use the boundary conditions to get a transcendental equation, and then that transcendental equation can be solved numerically. So I'm making a few assumptions in this problem: 1. The potential ##V(x)## is even, so the wavefunction ##\psi(x)## is either even or...
15. ### Determining Electric and Magnetic field given certain conditions

I am unsure of my solutions and am looking for some guidance. a.)The real part of the wave in complex notation can be written as ##\widetilde{A} = A^{i\delta}##. Writing the Complex Wave equation, we have ##\vec E(t) = \widetilde{A}e^{(-kz-\Omega t)} \hat x##. Therefore the real part is ##\vec...
16. ### A Solve the heat equation having Dirichlet boundary conditions

I am going through these notes...they are pretty easy to follow. I would like more insight on the initial condition. In this problem, (attachment below), i guess the choice of initial condition is convenient as its easier to plug in the values of ##n=2## and ##b=3## (highlighted on the...
17. ### I Query on Electromagnetic Theory (Dielectric Boundary Conditions)

The given question from Electromagnetic Theory (which is based on Dielectric Boundary Conditions) is as follows: Interface b/w two dielectric medium has a surface charge density (suppose xyz C / (m ^ 2) ). Using boundary condition find field in 1 (relative permittivity =xyz) if field in 2...
18. ### MATLAB No End" Boundary Conditions in Wave on a String

How did they impose boundary conditions here if "no end" is selected? Here: https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html I would like to do the same thing without changing the wave equation of the string.
19. ### MATLAB Boundary conditions in the resolution of a PDE with the FFT method

How to impose boundary conditions when solving a PDE with fft? For example here: If I copy this code I get periodic boundary conditions. Thank you
20. ### Engineering Hand tool boundary conditions - Forces determination

Hello, I' m trying to make a linear static analysis (Finite Element Analysis) on the following hand tool. I want to determine the boundary conditions. In order to do that I have decided to use a force couple to represent the forces that a bolt exerts on the jaws of this spanner. Despite using...
21. ### MOS Capacitor under very large positive or negative bias conditions

In MOSCAP, why does the band stop bending as soon as the Si Fermi level touches either the conduction band (inversion) or the valance band (accumulation)?
22. ### Conditions inside a protoplanetary disc

Summary:: Conditions inside a protoplanetary disc. I have just finished writing a fictional story that takes place inside a protoplanetary disc. Now I think I should determine how realistic it is. My question -- Somewhere in a typical PP disc, the gas pressure would be in the range of one...
23. ### Why heat PDE solution does not fully satisfy initial conditions?

Hi, I am solving heat equation with internal heat sources both numerically and analytically. My graphs are nearly identical but! analytical one have problem at the beginning and at the end for my domain. Many people have used the same technique to solve it analytically and they got good answers...
24. ### I Energy conditions and non-physical phenomena

Is the inability to exceed the speed of light a consequence of general relativity? Is the fact that no energy is created from empty space a consequence of general relativity? Or are they both constructions deriving from the energy conditions imposed to have solutions to Einstein's equations that...
25. ### A Non-isothermal conditions in liquid-gas nitrogen homogeneous mixture

I am studying the cavitation theory proposed by...
26. ### MHB Combinatorics: Order in a line by 2 conditions

Hi all, I need some help with this one:There are 3 shapes of pasta: 1,2,3. In a box there are 3 packages of pasta of shape 1, with different weights: 300 gr, 400 gr, 500gr. In addition, there are 5 packages of paste of shape 2, with weights: 300gr, 350gr, 400gr, 500gr, 600gr, and 4 packages...
27. ### Boundary Conditions for an infinite rectangular pipe

Does setting up the problem symmetrically on this axis and the boundary conditions applied make sense? I don't believe I will have a problem solving for the potential inside, but i just want to make sure I have my B.C and axis correct before proceeding. EDIT: Or should this be a 2-D lapace...
28. ### Evaluating the boundary conditions for a rectangular pipe

I have attached an image of the pipe in the attachmnts. The pipe is parallel to z-axis form (-∞,∞) and sides of length a. So my boundary conditions for this problem are as follows 1.) V=0 at y=0 2.)V=0 at y=a 4.)∂v/∂x=0 @ x=0 3.)V0 @ x=a I am a little confused on the fourth boundary...

30. ### Proving three angles are equal if they satisfy two conditions

Problem Statement : I copy and paste the statement of the problem directly from the text. Attempt : I wasn't able to go far into the solution. Below is a rough attempt. ##\begin{equation*} \begin{split} \sin^2A-\sin A\sin B+\sin^2B-\sin B\sin C+\sin^2C-\sin C\sin A & = 0\\ \sin A(\sin A -...
31. ### Error when creating boundary conditions (OpenFOAM)

Let's give some context. I created a Mesh via snappyHexMesh and next I am setting the boundary conditions (BCs). First I copied the patches folder "createPatchDict" to my system's folder via the command "cp \$FOAM_ETC/caseDicts/mesh/manipulation/patches/createPatchDict ./system" Taking into...
32. ### Boundary conditions ##\vec{B}## and ##\vec{H}##

When asking for boundary conditions I'm wondering if this is enough in this situation to give ##\vec{\nabla} \cdot \vec{B} = 0 , B_{2\perp} - B_{1 \perp} = 0## ##\vec{\nabla} \cdot \vec{H} = - \vec{\nabla} \cdot \vec{M}, H_{2\perp} - H_{1 \perp} = - (M_{2\perp} - M_{1 \perp})## ##\vec{\nabla}...
33. ### Boundary conditions (E and D) for a dielectric sphere

Since there is no free charge ##\int_S \vec{D} \cdot d\vec{a} = 0## and ##\rho_f = 0## ##\sigma_f = 0## ##\vec{nabla} \cdot \vec{P} = 0## since P is a constant ##\rho_b = - \vec{nabla} \cdot \vec{P} = 0## For a simple surface we can find the boundary conditions for ##\vec{E}## using a Gauss'...
34. ### Wheatstone bridge and conditions for current to flow between 2 points

Hello, I was reflecting on the functioning of a balanced Wheatstone bridge circuit: Point C and D are at the same electric potential V (zero potential difference). Even if they are connected by an ideal zero resistance wire, current will not split at either node C or D to flow through that...
35. ### Are Old Weather Conditions Officially Tracked?

Any official (scientific, verified) tracking of old weather conditions that one can look up? Say, I wanted to know what the weather was like in Kentucky in the city of Lexington on October 24th, 1983. Is there some kind of official recorded archive to look such information up?
36. ### I Non-Homogeneous Robin Boundary conditions and Interpretations of Signs

I have been solving the constant coefficient 1D advection-diffusion equation ##\frac{\partial c}{\partial t} + v\frac{\partial c}{\partial x} = D\frac{\partial^2 c}{\partial x^2}## on ##0<x<L,t>0## with a variety of robin BC's. Namely $$vc + D\frac{\partial c}{\partial x} = J^f ~~at~~ x=L$$...
37. ### A Solving Laplace's equation in polar coordinates for specific boundary conditions

Hello everybody, Currently I am doing my master's thesis and I've encountered a physics problem which is very difficult for me to solve. The problem I have is finding equations for the magnetic scalar potential inside and outside a ferromagnetic wire for specific boundary conditions...
38. ### Impedance Matching: The mathematical Conditions for Matching Network

Assume we have a network consisting of a source with impedance ##Z_S## and load with impedance ##Z_L## and we want to perform impedance matching on them in order to obtain the maximum power transfer: Note that in practice there may occur sitations where causes more harm than profit (see eg...
39. ### I How weather conditions affect a golf shot

Please correct me if I'm well off the fairway with the following theory. We all know that atmospheric conditions (temperature, pressure, dewpoint, etc.) can affect many different bodies in motion, from aeroplanes to cars to golf balls. But in the case of a golf ball, exactly how big is the...
40. ### Mathematica Mathematica bug? (Solving PDEs when the initial conditions contain a derivative)

hello I own mathematica 10.02 it is virtually impossible to solve PDE's ,even with NDSolve,if the initial conditions contain a derivative I write Derivative[1,0] [0,x] == f[x] I mean the first t derivative of u[t,x] for x at t=0 is f[x] I own a book based on Mathematica 10.3 Even if a...
41. ### Confused About Boundary Conditions for ##y## and ##x##

I am going through this notes, i can follow quite well...my only issue is on the highlighted part...i thought that we had two boundary conditions for ##y## ( of which one of them is non homogenous) and two boundary conditions for ##x##( of which both are homogenous)...kindly clarify on this part...
42. ### Boundary conditions in Ansys

Hi, I have one question related to the boundary conditions I should apply in a Static Structural simulation for the following support. The support is subjected to the following loading conditions shown below...
43. ### I Unraveling Laplace's Equation: Exploring Valid Domains and Boundary Conditions

Hi! This thread might well be similar to: https://www.physicsforums.com/threads/thread-about-jacksons-classical-electrodynamics-3rd-edition.910410/ I'm self-studying Vanderlinde and having a great time. However, I think that I am conflating and confusing many different things. Let me just ask...
44. ### How can I calculate critical loading conditions for max flap extension?

Below shows the generic V-N diagram for most of the civil aircrafts. Now, I have the CFD results available for multiple combinations of angles of attack of the aircraft, with the deflection angle of the flap. I have to choose a couple, to input into my structural analysis of the flaps. How to...
45. ### Boundary conditions for 2 ropes fixed to a massless ring with a damper

Hi, I'm not quite sure if I'm correct. I need to find the boundary conditions for 2 ropes ##T_1 \mu_1, T_2 \mu_2## fixed at ##x=0## to a massless ring with a massless damper of force ##F_d - -bv_y## Here what I think, since the ring and the damper is massless ##\sum F_y = 0##. Thus, ##-T_1...
46. ### I Sufficient Conditions for Strong Cosmic Censorship

In a podcast with Sean Carroll and Roger Penrose (link :) ), it's briefly discussed that one can cook up certain unphysical examples of spacetimes in which SCC is violated. Indeed, in Harvey Reall's BH notes (link), it's written that: What is a sufficient set of restrictions required in order...
47. ### Solving a first order differential equation with initial conditions

Hello! Consider this ODE; $$x' = sin(t) (x+2)$$ with initial conditions x(0) = 1; Now I've solved it and according to wolfram alpha it is correct (I got the homogenous and the particular solution) $$x = c * e^{-cos(t)} -2$$ and now I wanted to plug in the initial conditions and this is...
48. ### Periodic boundary conditions -> Shouldn't supports hinder all motion?

Hello everyone, I am currently trying to understand periodic boundary conditions for the mechanical investigation of mechanical properties of a RVE. I found a good video explaining the theory behind it: But something is unclear to me: At the above linked time step, the individual conical...
49. ### Transfer function with initial conditions (DE)

I have a differential equation of the form y''(t)+y'(t)+y(t)+C = 0. I think this implies that there are non-zero initial conditions. Is it possible to write a transfer function for this system? This post...
50. ### Unusual boundary conditions in FEA software

For a 2D problem with unknown displacements u(x,y) and v(x,y), is it allowed to give such a set of BCs u(0,y)=1 and vy(0,y)=0, the former being a displacement BC, the latter being a force BC (vy is the y strain)? How is this implemented in FEA software?