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In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified
Basic solution (linear programming)
Basic_solution_(linear_programming)
Concept from linear programming
In the theory of linear programming, a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables. Geometrically, each BFS corresponds
Basic_feasible_solution
Mathematical optimization problem restricted to integers
integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is
Integer_programming
Method to solve optimization problems
and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization)
Linear_programming
Routines for performing common linear algebra operations
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations
Basic Linear Algebra Subprograms
Basic_Linear_Algebra_Subprograms
Algorithm for linear programming
Dantzig's simplex algorithm (or simplex method) is an algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex
Simplex_algorithm
Solving an optimization problem with a quadratic objective function
function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context refers
Quadratic_programming
Optimization technique for solving (mixed) integer linear programs
means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems
Cutting-plane_method
Branch of mathematics
Geometric algebra Linear programming Linear regression, a statistical estimation method Numerical linear algebra Outline of linear algebra Transformation
Linear_algebra
splitting Basic solution (linear programming) — solution at vertex of feasible region Fourier–Motzkin elimination Hilbert basis (linear programming) — set
List of numerical analysis topics
List_of_numerical_analysis_topics
Family of programming languages
BASIC (Beginner's All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages designed for ease of use. The
BASIC
American mathematician (1914–2005)
algorithm, an algorithm for solving linear programming problems, and for his other work with linear programming. In statistics, Dantzig solved two open
George_Dantzig
Optimizing objective functions that have constrained variables
of the hard constraints are linear and some hard constraints are inequalities, then the problem is a linear programming problem. This can be solved by
Constrained_optimization
Basic concepts of algebra
x^{2}} is written as "x^2". This also applies to some programming languages such as Lua. In programming languages such as Ada, Fortran, Perl, Python and Ruby
Elementary_algebra
Field of mathematics
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which
Numerical_linear_algebra
Applying operations to whole sets of values simultaneously
science, array programming refers to solutions that allow the application of operations to an entire set of values at once. Such solutions are commonly
Array_programming
Method for linear optimization
a bounded number of steps an optimal solution is found. However, there are examples of degenerate linear programs, on which the original simplex algorithm
Bland's_rule
Statistical modeling method
resources about Linear regression The Wikibook R Programming has a page on the topic of: Linear Models Wikimedia Commons has media related to Linear regression
Linear_regression
Polynomial equation whose integer solutions are sought
equation with integer coefficients, for which only integer solutions are of interest. A linear Diophantine equation equates the sum of two or more unknowns
Diophantine_equation
Topics referred to by the same term
of any solution is also a solution Linear code, an error-correcting code for which any linear combination of codewords is also a codeword Linear cryptanalysis
Linear_(disambiguation)
Framework for modeling optimization problems that involve uncertainty
stochastic programming methods have been developed: Scenario-based methods including sample average approximation Stochastic integer programming for problems
Stochastic_programming
Most widely known generalized inverse of a matrix
norm solution to a system of linear equations with multiple solutions. The pseudoinverse facilitates the statement and proof of results in linear algebra
Moore–Penrose_inverse
Optimization algorithm
in a diverse range of SQP methods. Sequential linear programming Sequential linear-quadratic programming Augmented Lagrangian method SQP methods have been
Sequential quadratic programming
Sequential_quadratic_programming
Properties of mathematical relationships
Linear actuator Linear element Linear foot Linear system Linear programming Linear differential equation Bilinear Multilinear Linear motor Linear interpolation
Linearity
Algorithm in graph theory
Mathematical Programming, 60 (1–3): 255–276, CiteSeerX 10.1.1.297.5730, doi:10.1007/bf01580615, S2CID 5838223 Chvatal, Vasek (1983). "20". Linear Programming. Macmillan
Network_simplex_algorithm
Algorithm for generating pseudo-randomized numbers
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear
Linear_congruential_generator
Optimization by removing non-optimal solutions to subproblems
1016/0004-3702(84)90004-3. LiPS – Free easy-to-use GUI program intended for solving linear, integer and goal programming problems. Cbc – (Coin-or branch and cut) is
Branch_and_bound
Combinatorial optimization method
of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are
Branch_and_cut
Method of mathematical optimization
\mathbf {x} \in \mathbb {R} ^{n}} designate a candidate solution (agent) in the population. The basic DE algorithm can then be described as follows: Choose
Differential_evolution
Mathematical algorithm for eliminating variables from a system of linear inequalities
algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph Fourier who proposed
Fourier–Motzkin_elimination
Mathematical problem in operations research
the knapsack problem. The problem can be formulated as an integer linear programming problem. A paper machine can produce an unlimited number of master
Cutting_stock_problem
System where changes of output are not proportional to changes of input
solutions of Finite-Duration, which can happen under specific conditions for some non-linear ordinary differential equations. The most common basic approach
Nonlinear_system
Differential equation containing derivatives with respect to only one variable
equations, they are generally approximated by linear differential equations for an easier solution. The few non-linear ODEs that can be solved explicitly are
Ordinary differential equation
Ordinary_differential_equation
minimizing a function. In this case, one can use mathematical programming, such as linear programming. In this scenario, simulation helps when the parameters
Simulation-based_optimization
a linear algebra (LAPACK & BLAS) framework, and a statistics package. BLAS (Basic Linear Algebra Subprograms) is a de facto application programming interface
List_of_numerical_libraries
Subfield of mathematical optimization
heuristic), branch-and-cut (uses linear optimisation to generate bounds), dynamic programming (a recursive solution construction with limited search window)
Combinatorial_optimization
Algorithm for solving linear programs
successfully used is the cutting stock problem. One particular technique in linear programming which uses this kind of approach is the Dantzig–Wolfe decomposition
Column_generation
Combinatorial optimization problem
problem is "linear" because the cost function to be optimized as well as all the constraints contain only linear terms. A naive solution for the assignment
Assignment_problem
Optimization algorithm
gradient descent can converge to the global solution. Gradient descent can be used to solve a system of linear equations A x − b = 0 {\displaystyle \mathbf
Gradient_descent
Concept in linear programming and mathematical optimization
In linear programming, reduced cost, or opportunity cost, is the amount by which an objective function coefficient would have to improve (so increase for
Reduced_cost
Mathematical statement that two values are not equal
a larger example. see Linear programming#Example. Computer support in solving inequations is described in constraint programming; in particular, the simplex
Inequation
Type of functional equation (mathematics)
choice of approach to a solution. Commonly used distinctions include whether the equation is ordinary or partial, linear or non-linear, and homogeneous or
Differential_equation
Matrix form in linear algebra
as reduced echelon form can be used to solve problems about the solution to the linear system A x = b {\displaystyle Ax=b} where x ∈ R n {\displaystyle
Hermite_normal_form
Numerical approximation algorithm
rounding errors, direct methods would deliver an exact solution (for example, solving a linear system of equations A x = b {\displaystyle A\mathbf {x}
Iterative_method
Evolutionary algorithm
expression programming (GEP) in computer programming is an evolutionary algorithm that creates computer programs or models. These computer programs are complex
Gene_expression_programming
Metaheuristic method for optimization problems
guaranteed bounds and the exact solution is proposed. Variable Neighborhood Branching The mixed integer linear programming (MILP) problem consists of maximizing
Variable_neighborhood_search
Java math library
Second Order Conic Programming SDP - Explanation of Semidefinite Programming SQP - Explanation of Sequential quadratic programming Interior Point Method
SuanShu_numerical_library
Optimization method
is typically at least linear (since the whole input must be processed). With this assumption, the recurrence has the solution T(n) = O(S(n)). This can
Prune_and_search
Algorithm for solving linear programming problems with special structure
Dantzig–Wolfe decomposition is an algorithm for solving (mixed integer) linear programming problems by exploiting their structure. It was originally developed
Dantzig–Wolfe_decomposition
Function acting on function spaces
equations whose solutions are functions that satisfy the equation). (see Operator (physics) for other examples) The most basic operators are linear maps, which
Operator_(mathematics)
Advanced method of process control
disturbance. This is the optimal solution to linear robust control problems, however it carries a high computational cost. The basic idea behind the min/max MPC
Model_predictive_control
Algorithm for finding zeros of functions
inverse of J. If the nonlinear system has no solution, the method attempts to find a solution in the non-linear least squares sense. See Gauss–Newton algorithm
Newton's_method
Programming language
Dartmouth BASIC is the original version of the BASIC programming language. It was designed by two professors at Dartmouth College, John G. Kemeny and Thomas
Dartmouth_BASIC
Armadillo is a linear algebra software library for the C++ programming language. It aims to provide efficient and streamlined base calculations, while
Armadillo_(C++_library)
Numerical method for solving physical or engineering problems
we have concrete formulae for a large but finite-dimensional linear problem whose solution will approximately solve the original BVP. This finite-dimensional
Finite_element_method
Competitive algorithm for searching a problem space
are explored in genetic programming and graph-form representations are explored in evolutionary programming; a mix of both linear chromosomes and trees
Genetic_algorithm
Any algorithm which solves the search problem
complex adaptive systems Linear search problem – Computational search problem No free lunch in search and optimization – Average solution cost is the same with
Search_algorithm
Optimization problem
are three main approaches to modelling the VRP using mixed-integer linear programming (MILP): Vehicle flow formulations—this uses integer variables associated
Vehicle_routing_problem
Branch of mathematics
any way for computing the solutions. Linear algebra starts with the study of systems of linear equations. An equation is linear if it can be expressed in
Algebra
Numerical computing environment and programming language
MATLAB's initial linear algebra programming in 1967 with his one-time thesis advisor, George Forsythe. This was followed by Fortran code for linear equations
MATLAB
Measure of the level of acidity or basicity of an aqueous solution
logarithmic scale used to specify the acidity or basicity of aqueous solutions. Acidic solutions (solutions with higher concentrations of hydrogen (H+) cations)
PH
Formula for systems of linear equations
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever
Cramer's_rule
Mathematical model for sequential decision making under uncertainty
{\displaystyle {\bar {V}}^{*}} , we could use the following linear programming model: Primal linear program(P-LP) Minimize g s.t g − ∑ j ∈ S q ( j ∣ i , a ) h
Markov_decision_process
Node ordering for directed acyclic graphs
find linear extensions of partial orders. By definition, the solution of a scheduling problem that includes a precedence graph is a valid solution to topological
Topological_sorting
if and only if v is a basic feasible solution of the linear system Ax ≤ b. The representation of a polyhedron by a set of linear inequalities is not unique
N-dimensional_polyhedron
Projection of data onto lower-dimensional manifolds
a semidefinite programming problem. Unfortunately, semidefinite programming solvers have a high computational cost. Like Locally Linear Embedding, it has
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
the integrodifferential radiative transfer equation (RTE), but an exact solution is usually impossible and even in the case of geometrically simple systems
Discrete_ordinates_method
Linear programming for Combinatorial optimization
The configuration linear program (configuration-LP) is a linear programming technique used for solving combinatorial optimization problems. It was introduced
Configuration_linear_program
solved as an integer linear program (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linear programming relaxation (LP) of the
Randomized_rounding
Problem in combinatorial optimization
{\displaystyle m[w]} to calculate, the running time of the dynamic programming solution is O ( n W ) {\displaystyle O(nW)} . Dividing w 1 , w 2 , … , w n
Knapsack_problem
Method in numerical analysis
and Solutions to Systems of Equations", E. L. Allgower and K. Georg, SIAM Review, Volume 22, 28—85, 1980. [A3] "An Algorithm for Piecewise-Linear Approximation
Numerical_continuation
Data structure holding key/value pairs
mappings. With this implementation, the time to perform the basic dictionary operations is linear in the total number of mappings. However, it is easy to
Associative_array
Local search algorithm
stops, it returns the best solution found during its execution. Fred Glover (1986). "Future Paths for Integer Programming and Links to Artificial Intelligence"
Tabu_search
Topics referred to by the same term
disorder Blow fill seal, a manufacturing technique Basic feasible solution, in linear programming Be File System, the native file system for the Be Operating
BFS
Interpreter that enables users to enter and run programs in the BASIC language
second version of Dartmouth BASIC supported matrices and matrix operations, useful for the solution of sets of simultaneous linear algebraic equations; MAT
BASIC_interpreter
Matrix decomposition method
converge to a solution and (ii) that the solution is the one needed. Unfortunately neither is guaranteed and must be verified. Non-linear least squares
Cholesky_decomposition
Polynomial equation of degree two
represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation
Quadratic_equation
Situation where total gains match total losses
all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted
Zero-sum_game
Parallel software library for linear algebra
Automatic program configuration NUMA aware hybrid implementation with MPI and OpenMP Exchangeable dense and sparse matrix storage formats Basic linear algebra
Lis_(linear_algebra_library)
Sequence of operations for a task
as into one of the following: Linear programming When searching for optimal solutions to a linear function bound by linear equality and inequality constraints
Algorithm
Mathematician and engineer
included linear programming, a Newtonian bracketing method of convex minimization, input optimization, and risk modeling of dynamic programming, and the
Adi_Ben-Israel
Method for mathematical optimization
there are criss-cross algorithms for linear-fractional programming problems, quadratic-programming problems, and linear complementarity problems. Like the
Criss-cross_algorithm
NP-hard problem in combinatorial optimization
who expressed the problem as an integer linear program and developed the cutting plane method for its solution. They wrote what is considered the seminal
Travelling_salesman_problem
Mathematical way of attaining a desired output from a dynamic system
generally nonlinear and therefore, generally do not have analytic solutions (e.g., like the linear-quadratic optimal control problem). As a result, it is necessary
Optimal_control
Concepts from linear algebra
In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by
Eigenvalues_and_eigenvectors
Optimization algorithms using quantum computing
F^{\dagger }F} is small. Semidefinite programming (SDP) is an optimization subfield dealing with the optimization of a linear objective function (a user-specified
Quantum optimization algorithms
Quantum_optimization_algorithms
Concept in mathematics
representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications
Sparse_approximation
Business analytics software company
problem types: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer nonlinear programming Global optimization
AIMMS
Numerical optimization method
minimized. Let x ∈ ℝn designate a position or candidate solution in the search-space. The basic RS algorithm can then be described as: Initialize x with
Random_search
these problems, Couenne uses a reformulation procedure and provides a linear programming approximation of any nonconvex optimization problem. Couenne is an
Couenne
Sequential model-based optimization of expensive black-box functions
objectives. These variants change how the probabilistic model, incumbent solution, and sampling criterion are defined. A typical Bayesian optimization procedure
Bayesian_optimization
Computer compiler optimization technique
register's use. Cavazos et al., for instance, proposed a solution where it is possible to use both the linear scan and the graph coloring algorithms. In this approach
Register_allocation
Programming language that uses first order logic
logic. Unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and rules
Prolog
American mathematician (1924–2021)
most uses of linear programming to prove extremal combinatorial theorems. Over his career Hoffman studied the class of integer programming problems that
Alan_J._Hoffman
Type of logical formula
logic programming, a Horn clause is a logical formula of a particular rule-like form that gives it useful properties for use in logic programming, formal
Horn_clause
Digital motion graphics and compositing software
animation. It also functions as a very basic non-linear editor, audio editor, and media transcoder. In 2019, the program won an Academy Award for scientific
Adobe_After_Effects
General-purpose programming language
character data type, structured programming (Fortran 77), array programming, modular programming, generic programming (Fortran 90), parallel computing
Fortran
Computing joint values of a kinematic chain from a known end position
moveit_opw_kinematics_plugin (ROS Wiki) [4] D. G. Luenberger. 1989. Linear and Nonlinear Programming. Addison Wesley. A. Aristidou, and J. Lasenby. 2011. FABRIK:
Inverse_kinematics
Standard for HDTV image encoding and signal characteristics
per unit of area. For efficiency reasons, the standard specifies a non-linear transformation of each component signal, resulting in ( E R ′ , E G ′ ,
Rec._709
Process of developing trajectory performance
computing an open-loop solution to an optimal control problem. It is often used for systems where computing the full closed-loop solution is not required, impractical
Trajectory_optimization
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
Male
English
 English form of French Basile, BASIL means "king." Also sometimes given as an herb name.
Female
Scottish
Variant spelling of Scottish Lilias, LILEAS means "lily."
Male
English
Irish Anglicized form of Gaelic Fionnbarr, FINBAR means "fair-headed."
Boy/Male
Hindu
King, Basil the herb
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Boy/Male
Bengali, Indian
Resolution
Boy/Male
Tamil
Basic, Foundation
Boy/Male
Hindu
Lingam
Boy/Male
Tamil
King, Basil the herb
Male
Greek
(ΑἰνÎας) Variant spelling of Greek AineÃas, AINEAS means "praiseworthy."
Male
Yiddish
 Variant spelling of Yiddish Lieber, LIBER means "beloved." Compare with another form of Liber.
Female
English
Variant spelling of English Linsey, LINSAY means "Lincoln's wetlands."
Boy/Male
Muslim
King, Basil the herb (1)
Surname or Lastname
English
English : habitational name from Lingart, Lancashire, or Lingards Wood in Marsden, West Yorkshire, both named from Old English līn ‘flax’ + garðr ‘enclosure’.
Boy/Male
Greek
Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....
Boy/Male
Tamil
Basic, Foundation
Boy/Male
Greek American English
Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....
Female
Hebrew
 Variant spelling of Hebrew Basya, BASIA means "daughter of God."
Surname or Lastname
English
English : variant of Lingard.French : occupational name for a maker of or dealer in linen goods, from Old French linge ‘linen (goods)’ (see Linge 1).
Surname or Lastname
English
English : metronymic from Line.
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
Boy/Male
Hindu
Female
Chinese
Yuan River ruler.
Boy/Male
Australian, French, Italian, Latin
The Lord's; Belonging to the Lord
Boy/Male
Tamil
Thunderbolt
Boy/Male
Hindu, Indian, Kannada, Telugu, Traditional
One who Leapt Across the Ocean
Boy/Male
British, Danish, English, Swedish
Revered; Man from Sebaste
Boy/Male
Tamil
Madhukanta | மதà¯à®•à®¾à®‚த
The Moon
Male
Chamoru
, water related name (?)
Boy/Male
Hebrew
My brother is a song.
Boy/Male
Indian
Love to All
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
a.
Descending in a direct line from an ancestor; hereditary; derived from ancestors; -- opposed to collateral; as, a lineal descent or a lineal descendant.
n.
The name given to several aromatic herbs of the Mint family, but chiefly to the common or sweet basil (Ocymum basilicum), and the bush basil, or lesser basil (O. minimum), the leaves of which are used in cookery. The name is also given to several kinds of mountain mint (Pycnanthemum).
a.
Linear.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
n.
The act of resolving or making clear; resolution; solution.
adv.
In a linear manner; with lines.
n.
The state of being dissolved or disintegrated; resolution; disintegration.
a.
Composed of lines; delineated; as, lineal designs.
n.
See Exsolution.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
n.
The act or process of solving; solution; as, the resolution of an equation or problem.
n.
The quantity contained in a basin.
n.
One who lines, as, a liner of shoes.
n.
To analyse, or determine the strength of, by means of standard solutions. Cf. Standardized solution, under Solution.
n.
The termination of a disease; resolution.
a.
Of or pertaining to barium; as, baric oxide.
n.
Adverse action of will; unwillingness; -- opposed to volition.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.