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Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
Method to solve optimization problems
be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear programming, which
Linear_programming
Solving an optimization problem with a quadratic objective function
linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context refers to a formal procedure
Quadratic_programming
Concept in integral mathematics
programming relaxation has a value differing from that of the unrelaxed 0–1 integer program. The linear programming relaxation of an integer program may
Linear_programming_relaxation
Problem optimization method
Dynamic programming (DP) is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s
Dynamic_programming
Subfield of convex optimization
Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified
Semidefinite_programming
Optimization technique for solving (mixed) integer linear programs
cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not
Cutting-plane_method
optimizer) a software package for linear programming, integer programming, nonlinear programming, stochastic programming, and global optimization. The "What's
List_of_optimization_software
Algebraic modeling language
among them: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer quadratic programming with or without
AMPL
Datum of integral data type
for writing integer literals in many programming languages: Many programming languages, especially those influenced by C, prefix an integer literal with
Integer_(computer_science)
Study of mathematical algorithms for optimization problems
transformed into a convex program. Integer programming studies linear programs in which some or all variables are constrained to take on integer values. This is
Mathematical_optimization
Optimization by removing non-optimal solutions to subproblems
This approach is used for a number of NP-hard problems: Integer programming Nonlinear programming Travelling salesman problem (TSP) Quadratic assignment
Branch_and_bound
Computer arithmetic error
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the
Integer_overflow
Software package
GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and
GNU_Linear_Programming_Kit
Branch of mathematical optimization
problems on graphs, matroids and other discrete structures integer programming constraint programming These branches are all closely intertwined however, since
Discrete_optimization
Algorithm for linear programming
"Simplex algorithms". In J. E. Beasley (ed.). Advances in linear and integer programming. Oxford Science. pp. 1–46. MR 1438309. Maros, István (2003). Computational
Simplex_algorithm
Formula for systems of linear equations
prove that an integer programming problem whose constraint matrix is totally unimodular and whose right-hand side is integer, has integer basic solutions
Cramer's_rule
Computer compiler optimization technique
S2CID 1820765. A Tutorial on Integer Programming Archived 2009-09-05 at the Wayback Machine Conference Integer Programming and Combinatorial Optimization
Register_allocation
Subfield of mathematical optimization
satisfaction problem Cutting stock problem Dominating set problem Integer programming Job shop scheduling Knapsack problem Metric k-center / vertex k-center
Combinatorial_optimization
Statistical optimization technique
visual attention, architecture configuration in deep learning, static program analysis, experimental particle physics, quality-diversity optimization
Bayesian_optimization
Optimization algorithm
the Limited Memory Method for Large Scale Optimization". Mathematical Programming B. 45 (3): 503–528. CiteSeerX 10.1.1.110.6443. doi:10.1007/BF01589116
Limited-memory_BFGS
Combinatorial optimization method
for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. Branch
Branch_and_cut
Numerical optimization algorithm
(1973). "On Search Directions for Minimization Algorithms". Mathematical Programming. 4: 193–201. doi:10.1007/bf01584660. S2CID 45909653. McKinnon, K. I.
Nelder–Mead_method
Optimization problem in mathematics
formulated as a quadratically constrained quadratic program. Since 0–1 integer programming is NP-hard in general, QCQP is also NP-hard. However, even for a
Quadratically constrained quadratic program
Quadratically_constrained_quadratic_program
Subfield of mathematical optimization
a convex quadratic function. Second order cone programming are more general. Semidefinite programming are more general. Conic optimization are even more
Convex_optimization
Mathematical combinatorial optimization method
combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear programming (MILP) problems with many variables. The
Branch_and_price
Solution process for some optimization problems
that deals with problems that are not linear. Let n, m, and p be positive integers. Let X be a subset of Rn (usually a box-constrained one), let f, gi, and
Nonlinear_programming
check convex hull (integer) affine hull integer projection computing the lexicographic minimum using parametric integer programming coalescing parametric
Integer_set_library
Local search algorithm
found during its execution. Fred Glover (1986). "Future Paths for Integer Programming and Links to Artificial Intelligence". Computers and Operations Research
Tabu_search
Optimization technique
6(8):11472 (2011). Glover, Fred (January 1986). "Future paths for integer programming and links to artificial intelligence" (PDF). Computers and Operations
Metaheuristic
Special case of discrete optimization
variables, rather than individual variables, as in ordinary mixed integer programming. Knowing that a variable is part of a set and that it is ordered
Special_ordered_set
Optimization software package for linear programming
by IBM. The IBM ILOG CPLEX Optimizer solves integer programming problems, very large linear programming problems using either primal or dual variants
CPLEX
Nearest integers from a number
returns the greatest integer less than or equal to x, written ⌊x⌋ or floor(x). Similarly, the ceiling function returns the least integer greater than or equal
Floor_and_ceiling_functions
Optimization algorithm
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods
Sequential quadratic programming
Sequential_quadratic_programming
Optimization method
target. However, some real-life applications (like Sequential Quadratic Programming methods) routinely produce negative or nearly-zero curvatures. This can
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Initial set of valid possible values
non-negative. In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible
Feasible_region
bases enable iterative solutions of linear and various nonlinear integer programming problems in polynomial time. They were introduced by Jack E. Graver
Graver_basis
Matrix form in linear algebra
x} is restricted to have integer coordinates only. Other applications of the Hermite normal form include integer programming, cryptography, and abstract
Hermite_normal_form
File format
(Mathematical Programming System) is a file format for presenting and archiving linear programming (LP) and mixed integer programming problems. The format
MPS_(format)
Sequence of locally optimal choices
of a dynamic programming algorithm. Uriel Feige notes that: [Greedy algorithms] may be viewed as the ultimate form of dynamic programming, in which only
Greedy_algorithm
Graph with tight clique-coloring relation
closely connected to the theory of linear programming and integer programming. Both linear programs and integer programs are expressed in canonical form as seeking
Perfect_graph
Algorithms for solving convex optimization problems
programming". Dokl. Akad. Nauk SSSR. 174 (1): 747–748. Zbl 0189.19504. Karmarkar, N. (1984). "A new polynomial-time algorithm for linear programming"
Interior-point_method
Class of algorithms that find approximate solutions to optimization problems
appropriate mathematical programming formulation (typically a convex programming) such as Linear programming, Semidefinite programming, etc, to obtain a relaxation
Approximation_algorithm
solutions, integer programming etc. Some versions of the map label placement problem can be formulated as multiple choices integer programming (MCIP) problems
Automatic_label_placement
Optimization problem in mathematics
rectangle packing problem for fixed sizes and orientations as an integer linear program. Further, constraints and variables can be added to minimize the
Rectangle_packing
example, a linear programming relaxation of an integer programming problem removes the integrality constraint and so allows non-integer rational solutions
Relaxation_(approximation)
Decidable first-order theory of the natural numbers with addition
PA is in P, and this extends to fixed-dimensional parametric integer linear programming. Because Presburger arithmetic is decidable, automatic theorem
Presburger_arithmetic
Method of solving linear programming problems
operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm. The Big M method extends the simplex
Big_M_method
Framework for modeling optimization problems that involve uncertainty
integers Chance constrained programming for dealing with constraints that must be satisfied with a given probability Stochastic dynamic programming Markov
Stochastic_programming
Optimization problem
vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet
Vehicle_routing_problem
Algorithm used to solve non-linear least squares problems
proofs". Proceedings of the Jet Propulsion Laboratory Seminar on Tracking Programs and Orbit Determination: 1–9. Wiliamowski, Bogdan; Yu, Hao (June 2010)
Levenberg–Marquardt_algorithm
Optimization problem
Conforti, Michele; Cornuéjols, Gérard; Zambelli, Giacomo (2014). Integer Programming. Graduate Texts in Mathematics. Vol. 271. doi:10.1007/978-3-319-11008-0
Optimal_facility_location
Programming language for experimentation or art
An esoteric programming language (sometimes shortened to esolang) or weird language is a programming language designed to test the boundaries of computer
Esoteric_programming_language
Optimizing objective functions that have constrained variables
optimization Constraint satisfaction problem (CSP) Constraint programming Integer programming Metric projection Penalty method Superiorization Rossi, Francesca;
Constrained_optimization
Optimization algorithm
forward–backward algorithm for monotone inclusions (which includes convex programming and variational inequalities). Gradient descent is a special case of
Gradient_descent
Attribute of data
the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers
Data_type
Machine learning and inference framework
works use an integer linear programming (ILP) solver to solve the decision problem. Although theoretically solving an Integer Linear Program is exponential
Constrained_conditional_model
Software for operations research
framework for solving mixed integer programs (MIPs) over heterogeneous networks. It can use CLP, CPLEX, XPRESS or other linear programming solvers to solve the
COIN-OR
Suite of mathematical modeling and optimization tools
programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP)
FICO_Xpress
Collective behavior of decentralized, self-organized systems
organisms in synthetic collective intelligence. Boids is an artificial life program, developed by Craig Reynolds in 1986, which simulates flocking. It was
Swarm_intelligence
Iterative method for minimizing convex functions
Atallah, CRC Press 1999, 31-1 to 31-37. V. Chandru and M.R.Rao, Integer Programming, Chapter 32 in Algorithms and Theory of Computation Handbook, edited
Ellipsoid_method
minimal set of integer vectors in C such that every integer vector in C is a conical combination of the vectors in the Hilbert basis with integer coefficients
Hilbert basis (linear programming)
Hilbert_basis_(linear_programming)
NP-hard problem in combinatorial optimization
Directed Graphs and Integer Programs", IBM Mathematical research Project (Princeton University) Dantzig, George B. (1963), Linear Programming and Extensions
Travelling_salesman_problem
Linear programming algorithm
Application to Upper Bounds in Integer Quadratic Optimization Problems, Proceedings of Second Conference on Integer Programming and Combinatorial Optimisation
Karmarkar's_algorithm
Class of logic puzzles
may be analyzed using graph-theoretic methods, by dynamic programming, or by integer programming. Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected
River_crossing_puzzle
Unsolved problem in computer science
problems in operations research are NP-complete, such as types of integer programming and the travelling salesman problem. Efficient solutions to these
P_versus_NP_problem
Class of algorithms for solving constrained optimization problems
[citation needed] Sequential quadratic programming Sequential linear programming Sequential linear-quadratic programming Open source and non-free/commercial
Augmented_Lagrangian_method
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Gradient_method
Extent to which a programming language discourages type errors
are not of the appropriate data type, e.g. trying to add a string to an integer. Type enforcement can be static (catching potential errors at compile time)
Type_safety
Numerical software
open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. Written in C++ and published
HiGHS_optimization_solver
Programming language
and procedural programming language, designed by Niklaus Wirth as a small, efficient language intended to encourage good programming practices using
Pascal_(programming_language)
Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization. LINGO is a
LINDO
Numerical approximation algorithm
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Iterative_method
Greatest integer less than or equal to square root
number theory, the integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal
Integer_square_root
Method of mathematical optimization
Multi-objective and many-objective algorithms Techniques for handling binary/integer variables Artificial bee colony algorithm CMA-ES Evolution strategy Genetic
Differential_evolution
American businessman
"47-779 – Quantum Integer Programming – CMU Fall 2020". bernalde.github.io. Retrieved 2021-10-30. "47-779/785 – Quantum Integer Programming and Quantum Machine
Sridhar_Tayur
Technique for finding an extremum of a function
approximate the probe positions of golden section search while probing only integer sequence indices, the variant of the algorithm for this case typically
Golden-section_search
Design pattern in functional programming to build generic types
In functional programming, monads are a way to structure computations as a sequence of steps, where each step not only produces a value but also some
Monad (functional programming)
Monad_(functional_programming)
Mathematical optimization software
(Mixed Integer Optimizer) is an integer programming solver which uses branch and bound algorithm. MINTO is a software system that solves mixed integer programming
MINTO
Mathematical set closed under positive linear combinations
Integer Programming. John Wiley & Sons. pp. 88–89. ISBN 9780471982326. Conforti, Michele; Cornuejols, Gerard; Zambelli, Giacomo (2014-11-15). Integer
Convex_cone
Object which stores memory addresses in a computer program
— Donald Knuth, Structured Programming, with go to Statements In computer science, a pointer is an object in many programming languages that stores a memory
Pointer (computer programming)
Pointer_(computer_programming)
Procedural programming language
might be. Depending on the context, the word was treated either as an integer or a memory address. As machines with ASCII processing became common, notably
B_(programming_language)
Methods in numerical computation
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Rosenbrock_methods
Optimization algorithm
1016/0041-5553(66)90114-5. Frank, M.; Wolfe, P. (1956). "An algorithm for quadratic programming". Naval Research Logistics Quarterly. 3 (1–2): 95–110. doi:10.1002/nav
Frank–Wolfe_algorithm
Optimization algorithm
convex problems by hill-climbing include the simplex algorithm for linear programming and binary search. To attempt to avoid getting stuck in local optima
Hill_climbing
Mathematical concept
programming Decision-making software Goal programming Interactive Decision Maps Multiple-criteria decision-making Multi-objective linear programming Multi-disciplinary
Multi-objective_optimization
Algorithm to compute the maximum flow in a flow network
Combinatorial Paradigms Approximation algorithm Dynamic programming Greedy algorithm Integer programming Branch and bound/cut Graph algorithms Minimum spanning
Edmonds–Karp_algorithm
this problem is unlikely to have pseudo-polynomial algorithm. The integer programming model is given by: In this model, e i {\displaystyle e_{i}} means
Talent_scheduling
Quantum physics-based metaheuristic for optimization problems
doi:10.1038/nature10012. PMID 21562559. S2CID 205224761. "Learning to program the D-Wave One". D-Wave Systems blog. Archived from the original on July
Quantum_annealing
Open source software suite by Google
developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP), and related
OR-Tools
General-purpose, object-oriented programming language
general-purpose, object-oriented programming language that adds Smalltalk-style message passing (messaging) to the C programming language. Originally developed
Objective-C
Type of algorithm for constrained optimization
Other nonlinear programming algorithms: Sequential quadratic programming Successive linear programming Sequential linear-quadratic programming Interior point
Penalty_method
Manufacturing management process
generate feasible and near-optimal production schedules. Mixed-integer linear programming (MILP) is widely used in APS for planning problems where decisions
Advanced planning and scheduling
Advanced_planning_and_scheduling
Optimization algorithm
1016/S0305-0548(03)00155-2. Secomandi, Nicola. "Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands".
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Mathematical algorithm
Wright, Stephen J. (2015). "Coordinate descent algorithms". Mathematical Programming. 151 (1): 3–34. arXiv:1502.04759. doi:10.1007/s10107-015-0892-3. S2CID 15284973
Coordinate_descent
languages, programming languages, and problem-specific formats. Most of the linear programming, integer programming and nonlinear programming solvers accept
NEOS_Server
Solver for linear programs
software command line utility and library for solving linear programming and mixed integer programming problems. It ships with support for two file formats,
Lp_solve
Graph drawing with vertices in horizontal layers
the number of vertices per layer) may be solved using linear programming. Integer programming procedures, although more time-consuming, may be used to combine
Layered_graph_drawing
Number in {..., –2, –1, 0, 1, 2, ...}
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations
Integer
File format for presenting and archiving mathematical programming problems
among them: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer quadratic programming with or without
Nl_(format)
INTEGER PROGRAMMING
INTEGER PROGRAMMING
Girl/Female
Danish, Finnish, German, Swedish
Guarded by Ing; Ing's Beauty; Ing's Place
Girl/Female
American, Australian, Danish, Finnish, German, Scandinavian, Swedish, Teutonic
Guarded by Ing; Ing is Beautiful; Daughter of Hero; Enclosure
Boy/Male
Norse
Son's army.
Boy/Male
Arabic, Muslim
To Wait
Boy/Male
German, Norse, Swedish
Guarded by Ing; Ing's Beauty
Boy/Male
Muslim
To wait
Female
Scandinavian
Scandinavian form of Old Norse Ingigerðr, INGEGERD means "Ing's enclosure."
Girl/Female
Scandinavian Teutonic Danish Swedish
Ing's abundance. Feminine of Ing who was Norse mythological god of the earth's fertility.
Female
Swedish
Swedish contracted form of Scandinavian Ingegerd, INGER means "Ing's enclosure."
INTEGER PROGRAMMING
INTEGER PROGRAMMING
Boy/Male
Celtic Gaelic American
From the gray fortress.
Boy/Male
Muslim
Powerful
Girl/Female
Australian, British, Christian, English, German, Greek, Hebrew, Latin
Calf; Star of the Sea
Male
English
Anglicized form of Chinese Kong Fu Zi. Kong is the surname, CONFUCIUS means "hole" or "opening." Fu is the generation name, meaning "husband, master, man," and Zi is the given name, meaning "son."
Boy/Male
Greek Shakespearean
Soldier in the Trojan War.
Girl/Female
Indian, Telugu
Marigold Flower
Boy/Male
Indian
Printing
Girl/Female
English
Modern name based on Jane or Jean; Based on Janai meaning 'God has answered. '.
Boy/Male
Muslim
Desire
Girl/Female
Celtic, German
Race of Women; White Wave
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
INTEGER PROGRAMMING
n.
One who inters.
n.
One who makes an entrance or beginning.
v. t.
To place in a tomb; to bury; to inter; to entomb.
imp. & p. p.
of Inter
n.
That number placed below the line in vulgar fractions which shows into how many parts the integer or unit is divided.
v. t.
To deposit, as a dead body, in the earth; to bury; to inter.
v. t.
To inter with funeral rites; to bury.
p. pr. & vb. n.
of Inter
v. t.
To deposit or inter in a chapel; to enshrine.
v. t.
To inter.
n.
One who gathers the vintage.
v. t.
To deposit and cover in the earth; to bury; to inhume; as, to inter a dead body.
n.
A complete entity; a whole number, in contradistinction to a fraction or a mixed number.
n.
One who makes an index.
v. t.
To inhume; to bury; to inter.
v. t.
To bury; to inter; to entomb; as, obscurely sepulchered.
n.
One who intends.
a.
Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
v. t.
To inter again.