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Branch of mathematical optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the
Discrete_optimization
Branch of optimization in applied mathematics
Continuous optimization is a branch of optimization in applied mathematics. As opposed to discrete optimization, the variables used in the objective function
Continuous_optimization
Subfield of mathematical optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the
Combinatorial_optimization
Problem of finding the best feasible solution
variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as
Optimization_problem
Topics referred to by the same term
structures without continuity Discrete optimization, a branch of optimization in applied mathematics and computer science Discrete probability distribution
Discrete
Study of mathematical algorithms for optimization problems
It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines
Mathematical_optimization
Study of discrete mathematical structures
differential geometry, discrete exterior calculus, discrete Morse theory, discrete optimization, discrete probability theory, discrete probability distribution
Discrete_mathematics
Iterative simulation method
4104-4109 Clerc, M. (2004). Discrete Particle Swarm Optimization, illustrated by the Traveling Salesman Problem, New Optimization Techniques in Engineering
Particle_swarm_optimization
Types of numerical variables in mathematics
mathematics and statistics, a quantitative variable may be continuous or discrete. If it can take on two real values and all the values between them, the
Continuous or discrete variable
Continuous_or_discrete_variable
for multi-objective optimization and multidisciplinary design optimization. LINDO – (Linear, Interactive, and Discrete optimizer) a software package for
List_of_optimization_software
American mathematician
Engineering in 2011 for theoretical and computational contributions to discrete optimization. He is known for his work on the traveling salesman problem and
William_J._Cook
Mathematical optimization theory
Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought
Robust_optimization
Branch of geometry that studies combinatorial properties and constructive methods
related to subjects such as finite geometry, combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry
Discrete_geometry
Academic journal
relevant to the field of operations research such as continuous optimization, discrete optimization, game theory, machine learning, simulation methodology, and
Mathematics of Operations Research
Mathematics_of_Operations_Research
Process of finding the optimal set of variables for a machine learning algorithm
hyperparameter optimization methods. Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian
Hyperparameter_optimization
Professor of Industrial and Systems Engineering
expert in Operations Research, specializing solving and modeling discrete optimization problems arising from applications in homeland security, disaster
Laura_Albert_(academic)
DOPE, or Discrete Optimized Protein Energy, is a statistical potential used to assess homology models in protein structure prediction. DOPE is based on
Discrete optimized protein energy
Discrete_optimized_protein_energy
Numerical software
"Benchmarks for optimization software". Decision tree for optimization software. March 2022. Retrieved 31 March 2022. "Optimization and Operational Research:
HiGHS_optimization_solver
Special case of discrete optimization
In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an
Special_ordered_set
Soviet and Ukrainian mathematician
optimization. He made significant contributions to nonlinear and stochastic programming, numerical techniques for non-smooth optimization, discrete optimization
Naum_Z._Shor
Algorithm for the travelling salesman problem
TSP. Discrete Applied Mathematics 117 (2002), 81–86. J. Bang-Jensen, G. Gutin and A. Yeo, When the greedy algorithm fails. Discrete Optimization 1 (2004)
Nearest_neighbour_algorithm
American mathematician
Michigan. He is known for his research in nonlinear discrete optimization and combinatorial optimization. Lee graduated from Stuyvesant High School in 1977
Jon_Lee_(mathematician)
Mathematical method for optimizing material layout under given conditions
the performance of the system. Topology optimization is different from shape optimization and sizing optimization in the sense that the design can attain
Topology_optimization
Optimization algorithm
numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Sequence of locally optimal choices
Greedy algorithms are often used to solve combinatorial optimization problems. If an optimization problem only depends on the partial solution of solving
Greedy_algorithm
Field of knowledge
common games, such as chess and poker, are discrete) Discrete optimization, including combinatorial optimization, integer programming, constraint programming
Mathematics
Overview of and topical guide to discrete mathematics
Mathematical logic – Subfield of mathematics Discrete optimization – Branch of mathematical optimization Set theory – Branch of mathematics that studies
Outline of discrete mathematics
Outline_of_discrete_mathematics
Process of developing trajectory performance
Discretize the trajectory optimization problem directly, converting it into a constrained parameter optimization problem, 2) Solve that optimization problem
Trajectory_optimization
Simulation-based optimization (also known as simply simulation optimization) integrates optimization techniques into simulation modeling and analysis
Simulation-based_optimization
Branch of mathematics
{\displaystyle g_{i}(x)\geqslant 0,i=1,\ldots ,r} . Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over
Global_optimization
Computer scientist
of computational biology, program synthesis, superoptimization, discrete optimization, and psychometrics. Notable research projects he has contributed
Pushmeet_Kohli
American computer scientist (1936–2023)
Computers, Prentice-Hall, Englewood Cliffs, N.J., 1979, 200 pages. Discrete Optimization Algorithms: With Pascal Programs (with M.M. Syslo and J. S. Kowalik)
Narsingh_Deo
American industrial engineer and mathematician (1938–2024)
National Academy of Engineering for fundamental contributions to discrete optimization and software design, and its practical applications to distribution
Ellis_L._Johnson
Austrian mathematician
Austrian mathematician. His research interests include discrete optimization, graph theory, applied discrete mathematics, and applied number theory. He earned
Rainer_Burkard
Optimization algorithm
The bacterial colony optimization algorithm is an optimization algorithm which is based on a lifecycle model that simulates some typical behaviors of
Bacterial_colony_optimization
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
Academic journal
results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas
Journal_of_Graph_Theory
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
Necessary condition for optimality associated with dynamic programming
programming equation (DPE) associated with discrete-time optimization problems. In continuous-time optimization problems, the analogous equation is a partial
Bellman_equation
Sequential model-based optimization of expensive black-box functions
Bayesian optimization is a sequential model-based strategy for global optimization of black-box objective functions whose evaluations are costly. It is
Bayesian_optimization
Academic journal
Pentahedral Prisms". Discrete & Computational Geometry. 36: 167–204. doi:10.1007/s00454-005-1214-y. "The Fulkerson Prize". Mathematical Optimization Society. Retrieved
Discrete & Computational Geometry
Discrete_&_Computational_Geometry
Overview of and topical guide to combinatorics
combinatorics Coding theory Combinatorial optimization Combinatorics and dynamical systems Combinatorics and physics Discrete geometry Finite geometry Phylogenetics
Outline_of_combinatorics
Method of partitioning data points into groups based on their similarity
Bagon and Galun that the optimization of the correlation clustering functional is closely related to well known discrete optimization methods. In their work
Correlation_clustering
Optimization problem
Research Institute on Discrete Optimization and Systems Applications of the Systems Science Panel of NATO and of the Discrete Optimization Symposium. Elsevier
Optimal_job_scheduling
Israeli mathematician
computer science, in 1992. His thesis, "Discrete Geometry, Group Representations and Combinatorial Optimization: an Interplay", was advised by Louis J
Shmuel_Onn
Demand optimization Destination dispatch — an optimization technique for dispatching elevators Energy minimization Entropy maximization Highly optimized tolerance
List of numerical analysis topics
List_of_numerical_analysis_topics
Metaheuristic
modification of local search or hill climbing methods for solving discrete optimization problems. Local search methods can get stuck in a local minimum
Iterated_local_search
Model-free reinforcement learning algorithm
Proximal policy optimization (PPO) is a reinforcement learning (RL) algorithm for training an intelligent agent. Specifically, it is a policy gradient
Proximal_policy_optimization
NP-hard problem in combinatorial optimization
of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally
Travelling_salesman_problem
Quantum computing company
performs a single mathematical operation, discrete optimization. Rainier uses quantum annealing to solve optimization problems. The D-Wave One was claimed
D-Wave_Systems
British computer scientist
1979. His research interests lie in theoretical computer science, discrete optimization and combinatorics. Currently, he focuses on the complexity of counting
Martin_Dyer
American computer scientist
publications spanning the fields of network optimization artificial intelligence discrete optimization, simulation optimization, and quantum-inspired computing,
Fred_W._Glover
American mathematician and statistician
research in mathematics included work on the bin covering problem (a discrete optimization problem), while her later work in statistics and biostatistics included
Susan_Assmann
programming languages to create custom mathematical optimization applications. It is designed to solve optimization problems that arise in areas of business, industry
LINDO
Computer simulation Discrete event simulation Discrete rate simulation Continuous simulation Reliability block diagram Process optimization Simulation in manufacturing
ExtendSim
Award for advancements in discrete mathematics
for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical
Fulkerson_Prize
Set-to-real map with diminishing returns
(2003), Combinatorial Optimization, Springer, ISBN 3-540-44389-4 Lee, Jon (2004), A First Course in Combinatorial Optimization, Cambridge University Press
Submodular_set_function
American computer scientist (1933–1994)
expert on combinatorial optimization and a founder of the field, the author of the widely used textbook Combinatorial Optimization: Networks and Matroids
Eugene_Lawler
Topics referred to by the same term
Opus, a subsidiary of WSP Global Wandering salesman problem, in discrete optimization, similar to the travelling salesman problem Waste stabilization
WSP
Collective behaviour of entities that swarm
colony optimization is a widely used algorithm which was inspired by the behaviours of ants, and has been effective solving discrete optimization problems
Swarm_behaviour
Operations research and management sciences award
to discrete optimization including his deep research on balanced and ideal matrices, perfect graphs and cutting planes for mixed-integer optimization. 2010
John_von_Neumann_Theory_Prize
Topics referred to by the same term
of encoding genes Special ordered set of type 2, a structure in discrete optimization This disambiguation page lists articles associated with the same
SOS2
Topics referred to by the same term
or 1,2-Dioleoyl-sn-glycero-3-phosphoethanolamine, a phospholipid Discrete optimized protein energy, a method of assessing homology models in protein structure
Dope
Dutch mathematician and computer scientist
Dutch mathematician and computer scientist, a professor of discrete mathematics and optimization at the University of Amsterdam and a fellow at the Centrum
Alexander_Schrijver
value). Optimization of this objective is carried out using some form of discrete or combinatorial optimization. Most campaign creatives are optimized statically
Dynamic_creative_optimization
Technique used in signal processing and data compression
and optimization requires substantial engineering effort to make best use, within its intrinsic limits, of available built-in hardware optimization. The
Discrete_cosine_transform
1979 classic textbook on computational complexity theory
Scheduling Problems Parameterized by Partial Order Width". DOOR 2016: Discrete Optimization and Operations Research. Lecture Notes in Computer Science. Vol
Computers_and_Intractability
Algorithm for finding the shortest paths in graphs
(2005). "On the history of combinatorial optimization (till 1960)" (PDF). Handbook of Discrete Optimization. Elsevier: 1–68. Cormen, Thomas H.; Leiserson
Bellman–Ford_algorithm
Problem optimization method
sub-problems. In the optimization literature, this relationship is called the Bellman equation. In terms of mathematical optimization, dynamic programming
Dynamic_programming
Measure of graph complexity
"Computing maximum stable sets for distance-hereditary graphs", Discrete Optimization, 2 (2): 185–188, doi:10.1016/j.disopt.2005.03.004, MR 2155518. Corneil
Clique-width
American scientist (born 1933)
discrete optimization problems based on the continuous-time dynamics using a Hopfield network with continuous activation function. The optimization problem
John_Hopfield
mathematical optimization problems of more than 12 different types, including linear programming, integer programming and nonlinear optimization. The server
NEOS_Server
Machine: Nonlinear Discrete Optimization, European Mathematical Society, x+137 pp., 2010 Shmuel Onn: Linear and nonlinear integer optimization, Online Video
Graver_basis
Field of machine learning
policy optimization (PPO), to produce outputs that the reward model scores highly. The reward model substitutes for human raters during optimization, so
Reinforcement_learning
Belgian computer scientist
transportation. He has developed several optimization technologies including CHIP, Numerica, the Optimization Programming Language (OPL—now an IBM product)
Pascal_Van_Hentenryck
Class of reinforcement learning algorithms
sub-class of policy optimization methods. Unlike value-based methods which learn a value function to derive a policy, policy optimization methods directly
Policy_gradient_method
Discrete-variable probability distribution
gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function
Probability_mass_function
Branch of mathematics concerning probability
space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic
Probability_theory
Branch of numerical optimization
Deterministic global optimization is a branch of mathematical optimization which focuses on finding the global solutions of an optimization problem whilst providing
Deterministic global optimization
Deterministic_global_optimization
Search algorithm or heuristic method to solve constraint satisfaction problems
of the assignment is known. Although artificial intelligence and discrete optimization had known and reasoned about Constraint Satisfaction Problems for
Min-conflicts_algorithm
American mathematician
major focus has been in the design and analysis of algorithms for discrete optimization problems. In particular, his work has highlighted the role of linear
David_Shmoys
Optimization by removing non-optimal solutions to subproblems
an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists
Branch_and_bound
Japanese computer scientist (born 1940)
special issue: Discrete Algorithms and Optimization, in Honor of Professor Toshihide Ibaraki at His Retirement from Kyoto University", Discrete Applied Mathematics
Toshihide_Ibaraki
Computational problem of graph theory
(1972-03-01). "A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem". Management
K_shortest_path_routing
Method for finding loopless paths
EL (1972). "A procedure for computing the k best solutions to discrete optimization problems and its application to the shortest path problem". Management
Yen's_algorithm
American chemical engineer (born 1949)
areas of discrete/continuous optimization, optimal synthesis and planning of chemical processes and energy systems, supply chain optimization, and optimization
Ignacio_Grossmann
Chronological table of metaheuristic algorithms
frog-leaping algorithm: a memetic meta-heuristic for discrete optimization". Engineering Optimization. 38 (2): 129–154. doi:10.1080/03052150500384759. ISSN 0305-215X
Table_of_metaheuristics
Quadratic fractional programming problem
Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred
Bilevel_optimization
Software for numerical solution of partial differential equations
-Re_{\theta }} transition model. Design Optimization: Gradient-based shape optimization using integrated continuous and discrete adjoint solvers. It utilizes algorithmic
SU2_code
Collection of random variables
processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier
Stochastic_process
American control theorist
the book Perturbation Analysis of Discrete Event Dynamic Systems. and the book "Ordinal Optimization - Soft Optimization for Hard Problems" (Springer 2007)
Yu-Chi_Ho
Shmuel (2008), "Convex Discrete Optimization", in Floudas, Christodoulos A.; Pardalos, Panos M. (eds.), Encyclopedia of Optimization, Vol. 1 (2nd ed.), Springer
Dickson's_lemma
American mathematician (born 1950)
to discrete optimization including his deep research on balanced and ideal matrices, perfect graphs and cutting planes for mixed-integer optimization".
Gérard_Cornuéjols
Czech mathematician (1897–1970)
Nešetřil, Jaroslav (2001). "Vojtěch Jarník's work in combinatorial optimization". Discrete Mathematics. 235 (1–3): 1–17. doi:10.1016/S0012-365X(00)00256-9
Vojtěch_Jarník
Optimization problem in computer science
Research Institute on Discrete Optimization and Systems Applications of the Systems Science Panel of NATO and of the Discrete Optimization Symposium. Elsevier
Parallel_task_scheduling
in 2000/2001. The Trottier Building opened in 2003. David Avis - Discrete optimization and computational geometry Claude Crépeau - Quantum computing and
McGill School of Computer Science
McGill_School_of_Computer_Science
Discrete Fourier transform algorithm
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform
Fast_Fourier_transform
American mathematician (1919–1985)
2005 paper "On the history of combinatorial optimization (till 1960). Handbook of Discrete Optimization (K. Aardal, G.L. Nemhauser, R. Weismantel, eds
Julia_Robinson
Approach to optimizing robustness to failure
doi:10.1080/00207548708919855. P. Kouvelis and G. Yu, 1997, Robust Discrete Optimization and Its Applications, Kluwer. B. Rustem and M. Howe, 2002, Algorithms
Info-gap_decision_theory
Problem in computer science
ISBN 978-3-540-65367-7. [1]: A Pascal program for solving the problem. From Discrete Optimization Algorithms with Pascal Programs by MacIej M. Syslo, ISBN 0-13-215509-5
Set_packing
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DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
DISCRETE OPTIMIZATION
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