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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
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
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
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
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
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
Method for linear optimization
Michael J. Todd (February 2002). "The many facets of linear programming". Mathematical Programming. 91 (3): 417–436. doi:10.1007/s101070100261. S2CID 6464735
Bland's_rule
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
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
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
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
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
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
Branch of mathematics
Geometric algebra Linear programming Linear regression, a statistical estimation method Numerical linear algebra Outline of linear algebra Transformation
Linear_algebra
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
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
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
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
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
Properties of mathematical relationships
Linear actuator Linear element Linear foot Linear system Linear programming Linear differential equation Bilinear Multilinear Linear motor Linear interpolation
Linearity
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
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
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
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
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
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
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
Algorithm in graph theory
problem Bazaraa, Mokhtar S.; Jarvis, John J.; Sherali, Hanif D. (2010). Linear Programming and Network Flows (4th ed.). Wiley. p. 453. Orlin, James B. (1997-08-01)
Network_simplex_algorithm
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
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
Optimization by removing non-optimal solutions to subproblems
integer linear programs. Evolutionary algorithm Alpha–beta pruning A. H. Land and A. G. Doig (1960). "An automatic method of solving discrete programming problems"
Branch_and_bound
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
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)
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
API/ABI. BLAS (Basic Linear Algebra Subprograms) is a application programming interface standard for libraries that perform basic linear algebra operations
List_of_numerical_libraries
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
these problems, Couenne uses a reformulation procedure and provides a linear programming approximation of any nonconvex optimization problem. Couenne is an
Couenne
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
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
Java math library
Second Order Conic Programming SDP - Explanation of Semidefinite Programming SQP - Explanation of Sequential quadratic programming Interior Point Method
SuanShu_numerical_library
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)
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
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
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
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 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
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
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
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
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)
1957 technique for modelling problems of decision making under uncertainty
programming (SDP) is a technique for modelling and solving problems of decision making under uncertainty. Closely related to stochastic programming and
Stochastic dynamic programming
Stochastic_dynamic_programming
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
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)
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
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
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
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
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
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
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
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
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
the lower half of a colon!) The system also included support for solution of linear differential equations via the Runge–Kutta method. The system was
Laning_and_Zierler_system
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
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
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
Statistical modeling method
independent variable) related via a linear combination. A linear model with exactly one explanatory variable is a simple linear regression; a model with two
Linear_regression
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
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
Mathematical puzzle game
used as an example of recursion when teaching programming. As in many mathematical puzzles, finding a solution is made easier by solving a slightly more general
Tower_of_Hanoi
Computer made in France circa 1960
and an incremental compiler for a programming language known as PAF, which bore resemblance to Fortran and BASIC. Alice Recoque played a role in its
CAB_500
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
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
Optimization technique
optimization approaches, such as algorithms from mathematical programming, constraint programming, and machine learning. Both components of a hybrid metaheuristic
Metaheuristic
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
Solution in cooperative games
proof relies on solving successive exponential-sized linear programs, by constructing dynamic-programming based separation oracles. In a minimum-cost spanning-tree
Nucleolus_(game_theory)
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
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
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
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
MPICH2 with a focus on Single Program/Multiple Data (SPMD) parallel programming style pbdSLAP --- bundles scalable dense linear algebra libraries in double
Programming with Big Data in R
Programming_with_Big_Data_in_R
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
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
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
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
data, since in this case efficient linear algebra routines can be used and many problems have an explicit solution. As a result, fewer methods currently
Unevenly_spaced_time_series
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
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
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
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
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
evolution strategies, genetic programming and evolutionary programming. In his book discussing the use of genetic programming for the optimization of complex
Genetic_operator
When every path in a control-flow graph must go through one node to reach another
pred(n) The direct solution is quadratic in the number of nodes, or O(n2). Lengauer and Tarjan developed an algorithm which is almost linear, and in practice
Dominator_(graph_theory)
Awarded every year by the American Mathematical Society
JSTOR 1969599. Lewy, Hans (1957). "An example of a smooth linear partial differential equation without solution". Annals of Mathematics. 66 (1): 155–158. doi:10
Leroy_P._Steele_Prize
API for graph data and graph operations
GrB_SUCCESS; } Basic Linear Algebra Subprograms (BLAS) LEMON Graph Library "GraphBLAS". graphblas.org. Retrieved 2021-12-04. "GraphBLAS: A Programming Specification
GraphBLAS
Standard for HDTV image encoding and signal characteristics
(E'_{Y},E'_{\mathit {CB}},E'_{\mathit {CR}})} which are linear combinations of the (non-linear) RGB coordinates ( E R ′ , E G ′ , E B ′ ) {\displaystyle
Rec._709
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
travel, tourism, insurance
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
BASIC SOLUTION-LINEAR-PROGRAMMING
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