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Algorithm for solving linear programming problems
In mathematical optimization, affine scaling is an algorithm for solving linear programming problems. Specifically, it is an interior point method, discovered
Affine_scaling
Geometric transformation that preserves lines but not angles nor the origin
affine transformation that fixes a point; the latter may be a homothety, rotations around the fixed point, a scaling, with possibly negative scaling factors
Affine_transformation
1989 Optimisation algorithm
system used to compute the affine scaling direction defined in the above, one can note that taking a full step in the affine scaling direction results in the
Mehrotra predictor–corrector method
Mehrotra_predictor–corrector_method
Linear programming algorithm
mathematician I. I. Dikin in 1967. The affine-scaling method can be described succinctly as follows. While applicable to small scale problems, it is not a polynomial
Karmarkar's_algorithm
In statistics, generalized iterative scaling (GIS) and improved iterative scaling (IIS) are two early algorithms used to fit log-linear models, notably
Generalized_iterative_scaling
Geometric transformation
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale
Scaling_(geometry)
Framework for multi-scale signal representation
regions of interest for subsequent affine shape adaptation to obtain affine invariant interest points or for determining scale levels for computing associated
Scale_space
Sequential model-based optimization of expensive black-box functions
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Bayesian_optimization
Sequence of locally optimal choices
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Greedy_algorithm
Optimization algorithm
constant by a factor of two and is an optimal first-order method for large-scale problems. For constrained or non-smooth problems, Nesterov's FGM is called
Gradient_descent
Optimization by removing non-optimal solutions to subproblems
Hazimeh, Hussein; Mazumder, Rahul; Saab, Ali (2020). "Sparse Regression at Scale: Branch-and-Bound rooted in First-Order Optimization". arXiv:2004.06152
Branch_and_bound
Algorithms for solving convex optimization problems
Interior point methods can be used to solve semidefinite programs. Affine scaling Augmented Lagrangian method Chambolle-Pock algorithm Karush–Kuhn–Tucker
Interior-point_method
Optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Hill_climbing
Form of Newton's method used in statistics
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Scoring_algorithm
Algorithm used to solve non-linear least squares problems
To make the solution scale invariant Marquardt's algorithm solved a modified problem with each component of the gradient scaled according to the curvature
Levenberg–Marquardt_algorithm
Optimizing objective functions that have constrained variables
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Constrained_optimization
Subfield of mathematical optimization
^{n}\to \mathbb {R} } , i = 1 , … , p {\displaystyle i=1,\ldots ,p} , are affine transformations, that is, of the form: h i ( x ) = a i ⋅ x − b i {\displaystyle
Convex_optimization
Optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Frank–Wolfe_algorithm
Subfield of mathematical optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Combinatorial_optimization
Solution process for some optimization problems
set of transportation methods, one or more of which exhibit economies of scale, with various connectivities and capacity constraints. An example would
Nonlinear_programming
Method of solving linear programming problems
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Big_M_method
Numerical approximation algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Iterative_method
Numerical optimization algorithm
fixed step along each dimension in turn. Thus the method is sensitive to scaling of the variables that make up x {\displaystyle \mathbf {x} } . Criteria
Nelder–Mead_method
Algorithm for finding zeros of functions
ISBN 3-540-35445-X. MR 2265882. P. Deuflhard: Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms, Springer Berlin (Series in Computational
Newton's_method
Methods in numerical computation
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Rosenbrock_methods
Optimization algorithm
numerically efficient. The scaling of the initial matrix γ k {\displaystyle \gamma _{k}} ensures that the search direction is well scaled and therefore the unit
Limited-memory_BFGS
Problem optimization method
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Dynamic_programming
Special case of discrete optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Special_ordered_set
Solving an optimization problem with a quadratic objective function
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Quadratic_programming
Optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Sequential quadratic programming
Sequential_quadratic_programming
Inequalities for inexact line search
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Wolfe_conditions
Algorithm for linear programming
Stone, Richard E.; Tovey, Craig A. (1991). "The simplex and projective scaling algorithms as iteratively reweighted least squares methods". SIAM Review
Simplex_algorithm
Mathematical optimization problem restricted to integers
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Integer_programming
Algorithm to compute the maximum flow in a flow network
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Edmonds–Karp_algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Meta-optimization
Optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Construct allowing differentiation of tangent vector fields of manifolds
In differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, so it permits tangent vector
Affine_connection
Optimization method
estimation problems. Notable proprietary implementations include: The large scale nonlinear optimization software Artelys Knitro implements, among others
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Optimization algorithm
Davidon-Fletcher-Powell (DFP), Broyden-Fletcher-Goldfarb-Shanno (BFGS), and Self-Scaling-Variable-Metric (SSVM) methods. Suggestions for further optimization of
Quasi-Newton_method
Solving multiple machine learning tasks at the same time
transfer of knowledge implies a sequentially shared representation. Large scale machine learning projects such as the deep convolutional neural network
Multi-task_learning
Method to solve optimization problems
defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polytope. A linear programming algorithm
Linear_programming
Study of mathematical algorithms for optimization problems
Sequential quadratic programming: A Newton-based method for small-medium scale constrained problems. Some versions can handle large-dimensional problems
Mathematical_optimization
Mathematical algorithm
increased interest in the use of coordinate descent with the advent of large-scale problems in machine learning, where coordinate descent has been shown competitive
Coordinate_descent
Optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Line_search
Technique for finding an extremum of a function
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Golden-section_search
Type of algorithm for constrained optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Penalty_method
Algorithm for solving linear programs
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Column_generation
Mathematical combinatorial optimization method
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Branch_and_price
Collective behavior of decentralized, self-organized systems
systems give rise to emergent behaviours which occur at many different scales, some of which are turning out to be both universal and robust. It has become
Swarm_intelligence
Linear programming algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Revised_simplex_method
Optimization technique for solving (mixed) integer linear programs
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Cutting-plane_method
Mathematical algorithm for eliminating variables from a system of linear inequalities
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Fourier–Motzkin_elimination
Concept in mathematics
Nemirovski, Arkadi (2012) Tutorial: mirror descent algorithms for large-scale deterministic and stochastic convex optimization.https://www2.isye.gatech
Mirror_descent
Theorem about hexagons and conics
an affine scaling. For example for a Steiner inellipse, where the Brianchon point is the centroid. Brianchon's theorem is true in both the affine plane
Brianchon's_theorem
Class of algorithms for solving constrained optimization problems
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Augmented_Lagrangian_method
Affine shape adaptation is a methodology for iteratively adapting the shape of the smoothing kernels in an affine group of smoothing kernels to the local
Affine_shape_adaptation
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Parallel_metaheuristic
suitable to large-scale optimization problems, for which efficient LP and EQP solvers are available, these problems being easier to scale than full-fledged
Sequential linear-quadratic programming
Sequential_linear-quadratic_programming
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Guided_local_search
Feature detection algorithm in computer vision
descriptor is invariant to uniform scaling, orientation, illumination changes, and partially invariant to affine distortion. This section summarizes
Scale-invariant feature transform
Scale-invariant_feature_transform
Computer compiler optimization technique
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Register_allocation
Central object in linear algebra; mapping vectors to vectors
origin fixed are linear, including rotation, scaling, shearing, reflection, and orthogonal projection; if an affine transformation is not a pure translation
Transformation_matrix
Term in mathematical optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Trust_region
non-uniform scaling, reflections, rotations, shears, and other similarities and some, but not all linear maps. All triangles are affine-regular. In other
Affine-regular_polygon
Iterative optimisation algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Powell's_dog_leg_method
Optimization technique
Duepmeier, Clemens; Hagenmeyer, Veit (2020-11-02), "A Generic Flexible and Scalable Framework for Hierarchical Parallelization of Population-Based Metaheuristics"
Metaheuristic
Local search algorithm
Glover (2005). "Data Structures and Ejection Chains for Solving Large Scale Traveling Salesman Problems". European Journal of Operational Research.
Tabu_search
Coordinate system using perpendicular axes
received specific names. An example of an affine transformation which is not Euclidean is given by scaling. To make a figure larger or smaller is equivalent
Cartesian_coordinate_system
Branch of mathematical optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Discrete_optimization
Class of algorithms that find approximate solutions to optimization problems
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Approximation_algorithm
Metaheuristic proposed by Xin-She Yang
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Firefly_algorithm
Quantum physics-based metaheuristic for optimization problems
manufactured by D-Wave Systems. Hybrid quantum-classic algorithms for large-scale discrete-continuous optimization problems were reported to illustrate the
Quantum_annealing
Subfield of convex optimization
the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semidefinite programming is a relatively new
Semidefinite_programming
Continuous function whose value increases to infinity
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Barrier_function
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Lemke's_algorithm
Algorithm for computing the maximal flow of a network
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Dinic's_algorithm
Optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Spiral_optimization_algorithm
Primal-Dual algorithm optimization for convex problems
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Chambolle–Pock_algorithm
Combinatorial optimization method
Giovanni (1991). "A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems". SIAM Review. 33 (1): 60–100. doi:10
Branch_and_cut
Algorithm in computer science
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Artificial bee colony algorithm
Artificial_bee_colony_algorithm
In the fields of computer vision and image analysis, the Harris affine region detector belongs to the category of feature detection. Feature detection
Harris_affine_region_detector
Concept in convex optimization mathematics
little storage. Subgradient projection methods are often applied to large-scale problems with decomposition techniques. Such decomposition methods often
Subgradient_method
Algorithm for finding a local minimum of a function
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Powell's_method
Population-based search algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Bees_algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Gradient_method
Method for mathematical optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Criss-cross_algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Biconvex_optimization
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Humanoid_ant_algorithm
Group of all affine transformations of an affine space
In mathematics, the affine group or general affine group of any affine space is the group of all invertible affine transformations from the space into
Affine_group
Optimization method
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Davidon–Fletcher–Powell formula
Davidon–Fletcher–Powell_formula
Concept in mathematics
Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine
Affine_arithmetic
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Bat_algorithm
Because of the limited-memory matrix, the trust-region L-SR1 algorithm scales linearly with the problem size, just like L-BFGS. Quasi-Newton method Broyden's
Symmetric_rank-one
Numerical optimization algorithm
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Berndt–Hall–Hall–Hausman algorithm
Berndt–Hall–Hall–Hausman_algorithm
Unit hypercube of variable dimension whose corners have been perturbed
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Klee–Minty_cube
American computer scientist
convergence of a variant of Karmarkar's algorithm that became known as the Affine-Scaling algorithm. Eventually it became known that I.I. Dikin, working in Siberia
Robert_J._Vanderbei
Chinese scientist and revolutionary (born 1961)
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Liu_Gang
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Successive parabolic interpolation
Successive_parabolic_interpolation
Algorithm in mathematical optimization
ISBN 978-3-540-87743-1. Goldberg, Andrew V (1997). "An Efficient Implementation of a Scaling Minimum-Cost Flow Algorithm". Journal of Algorithms. 22: 1–29. doi:10.1006/jagm
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Finding multiple solutions of a problem
(Frank–Wolfe) Subgradient method Linear and quadratic Interior point Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar Basis-exchange
Evolutionary multimodal optimization
Evolutionary_multimodal_optimization
travel, tourism, insurance
AFFINE SCALING
AFFINE SCALING
Female
English
 Variant spelling of English Aileen, ALINE means "little Eve." Compare with another form of Aline.
Male
English
English name, probably derived from the vocabulary word alpine, ALPINE means "of the Swiss Alps."
Girl/Female
Armenian
Valuable.
Girl/Female
Irish French
Beautiful.
Girl/Female
English Latin
Warm.
Female
English
English pet form of Latin Euphemia, EFFIE means "Well I speak."
Female
English
Variant spelling of English Aline, ALLINE means "little Eve."Â
Female
Scandinavian
Scandinavian form of Hebrew Adiyna, ADINE means "slender."
Girl/Female
German
Soldier. Army Man. from the Old German Hariman.
Girl/Female
French
May Jehovah add. Addition (to the family). A feminine form of Joseph.
Girl/Female
Irish
In charge.
Girl/Female
Latin
Red haired.
Male
English
Middle English form of Anglo-Saxon Ealdwine, ALDINE means "old friend."
Girl/Female
Irish American Celtic English French
Oath.
Female
French
 Contracted form of French Adeline, ALINE means "little noble." Compare with another form of Aline.
Female
Hebrew
Variant spelling of Hebrew Amina, AMINE means "faithful, trusted."
Girl/Female
French
Blond.
Girl/Female
Italian
Famous bearer: Alcine is mistress of alluring enchantments and sensual pleasures in the Orlando...
Male
English
Pet form of English Alfred, ALFIE means "elf counsel."
Female
English
Pet form of English Saffron, SAFFIE means "saffron (the spice)."
AFFINE SCALING
AFFINE SCALING
AFFINE SCALING
AFFINE SCALING
AFFINE SCALING
AFFINE SCALING
AFFINE SCALING
travel, tourism, insurance