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mathematical optimization and related fields, relaxation is a modeling strategy. A relaxation is an approximation of a difficult problem by a nearby problem
Relaxation_(approximation)
Concept in integral mathematics
implies that the approximation ratio in the linear programming relaxation might be bad, and it may be better to look for other approximation schemes for that
Linear_programming_relaxation
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems
Hardness_of_approximation
Method in mathematical optimization
In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization
Lagrangian_relaxation
Topics referred to by the same term
distribution Chemical relaxation methods, related to temperature jump Relaxation oscillator, a type of electronic oscillator Relaxation (approximation), a technique
Relaxation
Electrically insulating substance able to be polarised by an applied electric field
dielectric relaxation refers to the relaxation response of a dielectric medium to an external, oscillating electric field. This relaxation is often described
Dielectric
Class of algorithms that find approximate solutions to optimization problems
work by solving a convex relaxation of the optimization problem on the given input. For example, there is a different approximation algorithm for minimum
Approximation_algorithm
Decay of nuclear spin polarization in MRI and NMR
depend on the physical system, but a simple approximation called the BPP theory is widely used. Another relaxation mechanism is the electrostatic interaction
Relaxation_(NMR)
Markovian master equation of a quantum system weakly coupled to its environment
as the Redfield relaxation theory. There is a close connection to the Lindblad master equation. If a so-called secular approximation is performed, where
Redfield_equation
optimization Relaxation (approximation) — approximating a given problem by an easier problem by relaxing some constraints Lagrangian relaxation Linear programming
List of numerical analysis topics
List_of_numerical_analysis_topics
Technique in numerical linear algebra
In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization
Low-rank_approximation
Principle in mathematical optimization
time complexity in the historical cases. Convex duality Duality Relaxation (approximation) Boyd, Stephen P.; Vandenberghe, Lieven (2004). Convex Optimization
Duality_(optimization)
Numerical approximation algorithm
improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones. A specific
Iterative_method
Mathematical optimization concept
duality Duality Duality (optimization) Semidefinite programming Relaxation (approximation) Gärtner, Bernd; Matoušek, Jiří (2006). Understanding and Using
Dual_linear_program
Time-dependent magnetic phenomena
Néel relaxation theory is a theory developed by Louis Néel in 1949 to explain time-dependent magnetic phenomena known as magnetic viscosity[clarification
Néel_relaxation_theory
linear programs, other kinds of relaxations are sometimes used. For example, see Goemans' and Williamson's max-cut approximation algorithm, which is based on
Randomized_rounding
Iterative solving method
numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems. Relaxation methods were developed
Relaxation_(iterative_method)
Special function defined by an integral
positive values of x {\displaystyle x} , there is a divergent series approximation that can be obtained by integrating x e x E 1 ( x ) {\displaystyle xe^{x}E_{1}(x)}
Exponential_integral
Method of solving a linear system of equations
In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations
Successive_over-relaxation
Problem in computational complexity theory
linear program L: The following algorithm using that relaxation is an expected (1-1/e)-approximation: Solve the linear program L and obtain a solution O
Maximum satisfiability problem
Maximum_satisfiability_problem
The Cole–Davidson equation is a model used to describe dielectric relaxation in glass-forming liquids. The equation for the complex permittivity is ε ^
Cole–Davidson_equation
Mathematical optimization problem restricted to integers
unique optimum of the relaxation is ( 1.8 , 2.8 ) {\displaystyle (1.8,2.8)} with objective value of 2.8. If the solution of the relaxation is rounded to the
Integer_programming
Classical problem in combinatorics
It has been shown that its relaxation indeed gives a factor- log n {\displaystyle \scriptstyle \log n} approximation algorithm for the minimum set
Set_cover_problem
Problem in combinatorial optimization
algorithm using dynamic programming. There is a fully polynomial-time approximation scheme, which uses the pseudo-polynomial time algorithm as a subroutine
Knapsack_problem
Quantum chemistry rule regarding vibronic transitions
the momentum is zero. Classically, the Franck–Condon principle is the approximation that an electronic transition is most likely to occur without changes
Franck–Condon_principle
Theorem in quantum mechanics
wavefunction.[citation needed] The two main sources of error are orbital relaxation, which refers to the changes in the Fock operator and Hartree–Fock orbitals
Koopmans'_theorem
Theory of laser diodes
Hartree–Fock approximation leads to absorption below the bandgap (below about 0.94 eV), which is a natural consequence of the relaxation time approximation, but
Semiconductor_laser_theory
Iterative method used to solve a linear system of equations
). We denote x ( k ) {\displaystyle \mathbf {x} ^{(k)}} as the k-th approximation or iteration of x {\displaystyle \mathbf {x} } , and x ( k + 1 ) {\displaystyle
Jacobi_method
Fairness notion in fair item allocation
general instances, a substantial body of work has focused on approximations, relaxations, and restricted settings. For a parameter α ∈ [0,1], an allocation
Envy-freeness_up_to_any_item
Algorithm used for points in euclidean space
computer science, Lloyd's algorithm, also known as Voronoi iteration or relaxation, is an algorithm named after Stuart P. Lloyd for finding evenly spaced
Lloyd's_algorithm
Methods for numerical approximations
(in contrast to discrete mathematics), and typically use numerical approximation in addition to symbolic manipulation. Numerical analysis finds application
Numerical_analysis
Approximation method in quantum physics
Hartree–Fock's inability to capture London dispersion. Relaxation of the last two approximations give rise to many so-called post-Hartree–Fock methods
Hartree–Fock_method
Algorithm for finding zeros of functions
Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version
Newton's_method
On short connecting nets with added points
39 {\displaystyle \ln(4)+\varepsilon \leq 1.39} approximation using a linear programming relaxation and a technique called iterative, randomized rounding
Steiner_tree_problem
sparse signals using the techniques of ℓ 1 {\displaystyle \ell _{1}} -relaxation. The term "nullspace property" originates from Cohen, Dahmen, and DeVore
Nullspace_property
Subfield of convex optimization
are important tools for developing approximation algorithms for NP-hard maximization problems. The first approximation algorithm based on an SDP is due
Semidefinite_programming
Concept in mathematics
NP-Hard, its solution can often be found using approximation algorithms. One such option is a convex relaxation of the problem, obtained by using the ℓ 1 {\displaystyle
Sparse_approximation
Subset of a graph's vertices, including at least one endpoint of every edge
2 {\displaystyle 2} approximation algorithm for the minimum vertex cover problem. Furthermore, the linear programming relaxation of that ILP is half-integral
Vertex_cover
Class of problems in computer science
general approximation algorithm attains a 2-factor approximation for the weighted case. Using the technique of Linear programming relaxation, it is possible
Interval_scheduling
Capacity of a material to conduct heat
constant. Time variation due to phonon decay is described with a relaxation time (τ) approximation ( ∂ ⟨ n ⟩ ∂ t ) decay = − ⟨ n ⟩ − ⟨ n ⟩ 0 τ , {\displaystyle
Thermal conductivity and resistivity
Thermal_conductivity_and_resistivity
Form of magnetism
of temperature. The typical time between two flips is called the Néel relaxation time. In the absence of an external magnetic field, when the time used
Superparamagnetism
Phonosurgical technique
the vocal pitch by shortening the thyroid ala. In this thyroplasty, the relaxation of the vocal cords is done by antero-posterior shortening of the thyroid
Thyroplasty
Repetitive variation of some measure about a central value
Hartley oscillator Oscillistor Phase-shift oscillator Pierce oscillator Relaxation oscillator RLC circuit Royer oscillator Vačkář oscillator Wien bridge
Oscillation
Study of dynamics of the Earth
stress and the material's physical properties, especially the stress relaxation time scale. Rocks are structurally and compositionally heterogeneous and
Geodynamics
Quantum mechanical state change
_{\text{rad}}}}.} In nonradiative relaxation, the energy is released as phonons, more commonly known as heat. Nonradiative relaxation occurs when the energy difference
Spontaneous_emission
Filling in missing entries of a matrix
{\displaystyle N} with high probability, thus Bernoulli sampling is a good approximation for uniform sampling. Another simplification is to assume that entries
Matrix_completion
Debye relaxation Debye sheath Debye shielding Debye temperature, see also Debye model Lorenz–Mie–Debye theory Rayleigh–Gans–Debye approximation 30852
List of things named after Peter Debye
List_of_things_named_after_Peter_Debye
Method of solving differential equations
method (known as relaxation, which generally reduces short-wavelength error) by a global correction of the fine grid solution approximation from time to time
Multigrid_method
Interatomic potentials constructed by machine learning programs
University launched in 2020. OC20 comprises approximately 1.3 million DFT relaxations across 82 elements, designed to accelerate the discovery of catalysts
Machine-learned interatomic potential
Machine-learned_interatomic_potential
Quantum algorithm for integer factorization
integer approximation to 2 2 n j / r {\displaystyle 2^{2n}j/r} , which can be divided by 2 2 n {\displaystyle 2^{2n}} to get a decimal approximation for j
Shor's_algorithm
Chemical reaction between a fuel and oxygen
Chiavazzo, Eliodoro (2012). "Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method". Journal
Combustion
Procedure undertaken by transgender people
finding a person's most comfortable pitch range, using breath support and relaxation exercises, introducing voice strengthening warm-ups, stabilizing posture
Transgender_voice_therapy
Indian American professor of computer science (born 1957)
(2001), "Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation", Journal
Vijay_Vazirani
Study of mathematical algorithms for optimization problems
perturbation stochastic approximation (SPSA) method for stochastic optimization; uses random (efficient) gradient approximation. Methods that evaluate
Mathematical_optimization
Quantum mechanical system that interacts with a quantum-mechanical environment
common assumptions about the behavior of the bath. For example, a common approximation is that the bath is Markovian, or memoryless. Taking this assumption
Open_quantum_system
Method of data analysis
qualitative variables) Canonical correlation CUR matrix approximation (can replace of low-rank SVD approximation) Detrended correspondence analysis Directional
Principal_component_analysis
Gravitational loss of momentum and energy by bodies moving through surrounding matter
the orbits of stars to be randomized. This process is called violent relaxation and can change two spiral galaxies into one larger elliptical galaxy.
Dynamical_friction
Study of the evolution of a material's magnetization
electrons (electron-spin relaxation) Lattice vibrations (spin-phonon relaxation) Spin waves, magnons (spin-spin relaxation) Impurities (spin-electron
Magnetization_dynamics
theory) Lagrangian system Lagrangian mixing Lagrangian point Lagrangian relaxation Lagrangian submanifold Lagrangian subspace Nonlocal Lagrangian Proca lagrangian
List of things named after Joseph-Louis Lagrange
List_of_things_named_after_Joseph-Louis_Lagrange
Concept in physics
The second approximation is that only the lowest (zero-point) lattice vibration is excited. This is called the low temperature approximation and means
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
Concept in computational geometry
prove the approximation ratio. See also. Let C be a pseudo-disks-set with n objects and union complexity u. Using linear programming relaxation, it is possible
Maximum_disjoint_set
Technique in computed tomography
\lambda _{k}} is an optional relaxation parameter, of the range 0 < λ k ≤ 1 {\displaystyle 0<\lambda _{k}\leq 1} . The relaxation parameter is used to slow
Algebraic reconstruction technique
Algebraic_reconstruction_technique
German computer scientist
German theoretical computer scientist, working in approximation algorithms, hardness of approximation, sum of squares, and high-dimensional statistics
David_Steurer
Statistical analysis technique
regression framework, a penalized matrix decomposition framework, a convex relaxation/semidefinite programming framework, a generalized power method framework
Sparse_PCA
Geometric arrangement of a nodal group
nodal group that relates to the point of interest by using a numerical approximation routine. Stencils are the basis for many algorithms to numerically solve
Stencil_(numerical_analysis)
Device that compares two voltages or currents
analog signals, such as analog-to-digital converters (ADCs), as well as relaxation oscillators. The differential voltages must stay within the limits specified
Comparator
Movement of entangled polymer chains
viscosity gives an approximation of the actual observed dependency, τ ∝ M3.4; this relaxation time has nothing to do with the reptation relaxation time. Entangled
Reptation
Transition rate formula
part of a continuum, if there is some decoherence in the process, like relaxation or collision of the atoms, or like noise in the perturbation, in which
Fermi's_golden_rule
Stochastic process modeling random walk with friction
X_{t}=e^{-2t}W_{e^{4t}}} . The Ornstein–Uhlenbeck process is a prototype of a noisy relaxation process. A canonical example is a Hookean spring (harmonic oscillator)
Ornstein–Uhlenbeck_process
Markovian quantum master equation for density matrices (mixed states)
operators can be included to model various forms of dephasing and vibrational relaxation. These methods have been incorporated into grid-based density matrix propagation
Lindbladian
Description of particle density in statistical mechanics
equation, using approximative closure relations like the Percus–Yevick approximation or the hypernetted-chain theory. It can also be determined experimentally
Radial_distribution_function
Combinatorial optimization method
to tighten the linear programming relaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called cut and branch
Branch_and_cut
Combinatorial optimization problem
However, there are linear-programming relaxations which give a ( 1 − 1 / e ) {\displaystyle (1-1/e)} -approximation. For the problem variant in which not
Generalized assignment problem
Generalized_assignment_problem
Iterative method in numerical analysis
{\displaystyle \alpha _{k}} sum to one, we can make the first order approximation g ( X k α k ) = g ( ∑ i = 0 m k ( α k ) i x k − m k + i ) ≈ ∑ i = 0
Anderson_acceleration
Algorithmic determination of wave cycle parts
can recover signal x {\displaystyle \mathbf {x} } by best rank-one approximation. Phase retrieval is a key component of coherent diffraction imaging
Phase_retrieval
Graph used in computational complexity theory and graph theory
of its semidefinite relaxation. According to the unique games conjecture, for many problems such as this the optimal approximation ratio is provided by
Frankl–Rödl_graph
~U=\theta L~} is rate of relaxation of photons in the laser cavity, V = 1 / τ {\displaystyle ~V=1/\tau ~} is rate of relaxation of excitation of the gain
Self-pulsation
Property of materials with both viscous and elastic characteristics under deformation
each mode of the relaxation, g i {\displaystyle g_{i}} is the relaxation modulus and θ i {\displaystyle \theta _{i}} is the relaxation time; h ( I 1 ,
Viscoelasticity
Method in physics
{\displaystyle \nu _{n}} is the frequency of the phonon. Making the approximation that the frequency is inversely proportional to the wavelength, E n
Debye_model
American molecular biologist and physicist (1929–2019)
American physicist and biochemist. In 1955 he published the Redfield relaxation theory, effectively moving the practice of NMR or Nuclear magnetic resonance
Alfred_G._Redfield
Vehicle emission standards
adapting to technical progress Council Directive 70/156/EEC on the approximation of the laws of the Member States relating to the type-approval of motor
European_emission_standards
Numerical simulations of physical problems via computers
numerical approximations are required. Computational physics is the subject that deals with these numerical approximations: the approximation of the solution
Computational_physics
Diminished responsiveness to a stimulus after repeated exposure
from least to most disturbing. By using techniques that produce deep relaxation, an individual can then confront each phobia in scenes of increasing intensity
Desensitization_(psychology)
Model of electrons within a metallic solid
fields in metals are weak because of the screening effect. Relaxation-time approximation: There is some unknown scattering mechanism such that the electron
Free_electron_model
Iterative method used to solve a linear system of equations
k} -th approximation or iteration of x {\displaystyle \mathbf {x} } , and by x ( k + 1 ) {\displaystyle \mathbf {x} ^{(k+1)}} the approximation of x {\displaystyle
Gauss–Seidel_method
Model of electrical conduction
theory of metals. This is because metals have essentially a better approximation to the free electron model, i.e. metals do not have complex band structures
Drude_model
Measure of positive and negative charges
sometimes called the point dipole approximation, the discrete dipole approximation, or simply the dipole approximation. Not to be confused with the magnetic
Electric_dipole_moment
Physical system that responds to a restoring force proportional to displacement
order τ = 1/(ζω0). In physics, the adaptation is called relaxation, and τ is called the relaxation time. In electrical engineering, a multiple of τ is called
Harmonic_oscillator
Specific probability distribution function, important in physics
like an ideal gas and the Maxwell speed distribution is an excellent approximation for such gases. This is also true for ideal plasmas, which are ionized
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Subfield of mathematical optimization
Springer-Verlag. ISBN 978-3-540-15642-0. Lemaréchal, Claude (2001). "Lagrangian relaxation". In Michael Jünger and Denis Naddef (ed.). Computational combinatorial
Convex_optimization
Equations in quantum field theory
superconducting order; τ {\displaystyle \tau } the temperature-dependent GL relaxation time of the order parameter; V {\displaystyle V} the electrochemical potential;
Time-dependent Ginzburg–Landau theory
Time-dependent_Ginzburg–Landau_theory
Algorithm for finding the shortest paths in graphs
cycle. Like Dijkstra's algorithm, Bellman–Ford proceeds by relaxation, in which approximations to the correct distance are replaced by better ones until
Bellman–Ford_algorithm
ε) approximation algorithm for the Steiner tree problem on such instances. Subsequently, the ε factor was removed by Rizzi and a 4/3 approximation algorithm
Quasi-bipartite_graph
{1e} }} and T 1 n {\displaystyle T_{\mathrm {1n} }} are the spin-lattice relaxation time for the electron and the nucleus respectively. T 2 e {\displaystyle
Electron nuclear double resonance
Electron_nuclear_double_resonance
American mathematician
factor approximation algorithm for the Generalized Assignment Problem and Unrelated Parallel Machine Scheduling. Constant factor approximation algorithm
David_Shmoys
Calculation of complex statistical distributions
particle approximations. Springer. p. 575. Del Moral, Pierre; Miclo, Laurent (2000). "Branching and Interacting Particle Systems Approximations of Feynman-Kac
Markov_chain_Monte_Carlo
Statistical mechanics model for ultrafast carrier relaxation
physics, this model is used to describe the process of ultrafast carrier relaxation following excitation. Such dynamics is so fast that, in order to probe
Two_temperature_model
Property of light sources related to black-body radiation
lower color temperature) light is often used in public areas to promote relaxation, while a cooler (higher color temperature) light is used to enhance concentration
Color_temperature
Charge transfer due to contact or sliding
charging due to air-blown particles; demonstrated that surface strain and relaxation played a critical role for a range of materials, and examined the tribocharging
Triboelectric_effect
Fair item allocation problem
{\log {n}}})} -approximation algorithm, based on rounding a linear program. Feige proved that a polynomial-time constant-factor approximation algorithm exists
Egalitarian_item_allocation
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION
Girl/Female
Biblical
Relaxation, physic, comfort.
Boy/Male
Indian, Telugu
Good Relation; Relationship with Friends and Neighberhood
Boy/Male
Indian
Of Husain, Nisba relation
Boy/Male
Tamil
Jasevaraj | ஜஸேவாராஜ
Heart of relation
Jasevaraj | ஜஸேவாராஜ
Boy/Male
Tamil
Relation
Boy/Male
Assamese, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Friend; Relation
Girl/Female
Hindu, Indian
Friendship; Good Relation
Girl/Female
Arabic, Muslim
Relation; Way; Sake
Biblical
Raphu, relaxation; physic; comfort
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Rest; Relaxation
Boy/Male
Indian
Relation
Boy/Male
Muslim
Of Husain, Nisba relation
Girl/Female
Hindu, Indian
Relation
Boy/Male
Hindu, Indian
Relation; Connection
Boy/Male
Hindu, Indian
Relation
Girl/Female
Biblical
Relaxation, physic, comfort.
Boy/Male
Hindu, Indian
Leader; Relation
Boy/Male
Hindu, Indian
Heart of Relation
Girl/Female
Muslim
Relation, Way, Sake
Girl/Female
Tamil
Vishranti | விஷà¯à®°à®¾à®‚தி
Rest, Relaxation
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION
RELAXATION APPROXIMATION