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Type of multi-objective optimization
Lexicographic optimization is a kind of multi-objective optimization. In general, multi-objective optimization deals with optimization problems with two
Lexicographic_optimization
Optimization method
Lexicographic max-min optimization (also called lexmaxmin or leximin or leximax or lexicographic max-ordering optimization) is a kind of multi-objective
Lexicographic max-min optimization
Lexicographic_max-min_optimization
Generalised alphabetical order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order
Lexicographic_order
Concept in economics
In economics, lexicographic preferences or lexicographic orderings describe comparative preferences where an agent prefers any amount of one good (X) to
Lexicographic_preferences
Mathematical concept
Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute
Multi-objective_optimization
Lipschitz constant of the objective function. Lexicographic max-min optimization - a different kind of optimization problem (multi-objective rather than single
Min-max_optimization
Topics referred to by the same term
a flamethrower built by the Soviet Union Law practice optimization Landing Page Optimization Leading Petty Officer Legal Process Outsourcing Leningrad
LPO
matching. It could be called lexicographic rank-egalitarian stable matching. It is similar to lexicographic max-min optimization (leximin) of the utility
Optimal_stable_matching
Approach to portfolio selection under loss aversion
management § Investment management Kelly criterion Lexicographic preferences Loss aversion Portfolio optimization Post modern portfolio theory Roy's safety-first
Chance-constrained portfolio selection
Chance-constrained_portfolio_selection
Branch of multiobjective optimization
levels. This is known as lexicographic or pre-emptive goal programming. Ignizio gives an algorithm showing how a lexicographic goal programme can be solved
Goal_programming
Increasing execution speed and reducing the overheads associated with loops
representations of the computation being optimized and the optimization(s) being performed. Loop optimization can be viewed as the application of a sequence
Loop_optimization
Mathematical method
1090/conm/636/12729 E. Bonacker, A. Gibali, K-H. Küfer and P. Süss, Speedup of lexicographic optimization by superiorization and its applications to cancer radiotherapy
Superiorization
Research unit of UC Irvine
Jayakrishnan formulated the vehicle reidentification problem as a lexicographic optimization problem and demonstrated robust performance 2000 – David Brownstone
UC Irvine Institute of Transportation Studies
UC_Irvine_Institute_of_Transportation_Studies
Search tree data structure
various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A notable optimization is
Trie
Part of a computer program where a given name binding is valid
particular variables. However, Maclisp treated lexical binding more as an optimization than one would expect in modern languages, and it did not come with the
Scope_(computer_programming)
Algorithm that arranges lists in order
numerical order and lexicographical order, and either ascending order or descending order. Efficient sorting is important for optimizing the efficiency of
Sorting_algorithm
Comparison between vectors
represent the leximin order. The same is true for the lexicographic order. Lexicographic max-min optimization is the computational problem of finding a maximal
Leximin_order
Weakly optimal allocation of resources
harming other variables in the subject of multi-objective optimization (also termed Pareto optimization). Some economists consider the Pareto efficiency principle
Pareto_efficiency
Database class for storage and retrieval of modeled data
can be extended to a discretely ordered model that maintains keys in lexicographic order. This extension is computationally powerful, in that it can efficiently
NoSQL
point search: an optimization to A* which may reduce computation time by an order of magnitude using further heuristics Lexicographic breadth-first search
List_of_algorithms
Data structure
a given string, by lexicographic order. Find successor: Locates the smallest string greater than a given string, by lexicographic order. The data structure
Radix_tree
Non-comparative lexicographical sorting algorithm
LSD Radix sort. Optimized radix sorts can be very fast when working in a domain that suits them. They are constrained to lexicographic data, but for many
Radix_sort
Computing operation which compares two values
common library function strcmp in C and related languages is a three-way lexicographic comparison of strings; however, these languages lack a general three-way
Three-way_comparison
convex hull (integer) affine hull integer projection computing the lexicographic minimum using parametric integer programming coalescing parametric vertex
Integer_set_library
or convex bodies. Six kinds of problems are particularly important: optimization, violation, validity, separation, membership and emptiness. Each of these
Algorithmic problems on convex sets
Algorithmic_problems_on_convex_sets
Process for converting data into a "standard", "normal", or canonical form
is performed Lexicographic order is imposed on the namespace declarations and attributes of each element In morphology and lexicography, a lemma is the
Canonicalization
Quasi-infinite number in mathematics
cellular automata. In optimization, Marco Cococcioni, Massimo Pappalardo, and Sergeyev proposed a grossone-based method for lexicographic multi-objective linear
Grossone
Practice search engine optimization
Keyword clustering is a practice search engine optimization (SEO) professionals use to segment target search terms into groups (clusters) relevant to each
Keyword_clustering
Operations research that evaluates multiple conflicting criteria in decision making
Combinatorial Optimization – Theory, Methodology, and Applications". In Ehrgott, Matthias; Gandibleux, Xavier (eds.). Multiple Criteria Optimization: State of
Multiple-criteria decision analysis
Multiple-criteria_decision_analysis
List of concepts in artificial intelligence
stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. Stochastic optimization methods
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Linear programming algorithm
In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming. The revised simplex method
Revised_simplex_method
Problem-solving method
substantial consequence was that computational models of heuristics, such as lexicographic rules (Fishburn, 1974) and elimination-by-aspects (Tversky, 1972), became
Heuristic
Theorem in order and lattice theory
fixed-point. They consider two kinds of lattices: componentwise ordering and lexicographic ordering. They consider two kinds of input for the function f: value
Knaster–Tarski_theorem
Scheme for controlling errors in data over noisy communication channels
range of possible code rates, which can be optimized depending on the scenario. Usually, this optimization is done in order to achieve a low decoding
Error_correction_code
Solution in cooperative games
nucleolus of a general game can be computed by any algorithm for lexicographic max-min optimization. These algorithms usually require to solve linear programs
Nucleolus_(game_theory)
Mathematical ranking of a set
science, in partition refinement based algorithms for lexicographic breadth-first search and lexicographic topological ordering. In these algorithms, a weak
Weak_ordering
Rawlsian decision rule for social choice
010. ISSN 0004-3702. Imai, Haruo (1983). "Individual Monotonicity and Lexicographic Maxmin Solution". Econometrica. 51 (2): 389–401. doi:10.2307/1911997
Egalitarian_rule
Data storage paradigm in computing
bytes to bytes. An OKVS will keep the key–value pairs sorted by the key lexicographic order. OKVS systems provides different set of features and performance
Ordered_key–value_store
Order of bytes in a computer word
28 March 2020. Retrieved 15 August 2018. "3.10 Options That Control Optimization: -fstrict-aliasing". GNU Compiler Collection (GCC). Free Software Foundation
Endianness
Algorithm used in data compression
matrix) whose rows are the circular shifts of the input text, sorted in lexicographic order, then taking the final column of that matrix. To allow the transform
Burrows–Wheeler_transform
Decision strategy
The priority heuristic is a simple, lexicographic decision strategy that helps decide for a good option. In psychology, priority heuristics correctly
Priority_heuristic
Method of counting votes and determining results
and subject to that the second-maximum load, etc. (using lexicographic max-min optimization). The load-balancing is done sequentially, in each round.
Phragmen's_voting_rules
Computational chemistry
identification and optimization. Since then, both terms, cheminformatics and chemoinformatics, have been used,[citation needed] although, lexicographically, cheminformatics
Cheminformatics
Measure of algorithmic complexity
a string can be computed by simply trying every halting program, in lexicographic order, until one of them outputs the string. The other direction is
Kolmogorov_complexity
Computational geometry concept
Sourd, Francis (2010), "Lexicographically minimizing axial motions for the Euclidean TSP", Journal of Combinatorial Optimization, 19 (1): 1–15, doi:10
Bitonic_tour
Historical dictionary of the English language
format of the OED's entries has influenced numerous other historical lexicography projects. The forerunners to the OED, such as the early volumes of the
Oxford_English_Dictionary
Fair division protocol in computing
The maximum x can be found by solving a linear program; see Lexicographic max-min optimization. Alternatively, the DRF can be computed sequentially. The
Dominant_resource_fairness
parameters are adaptively updated throughout the process, according to some optimization approach. The main difference between 1D and 2D adaptive filters is that
2D_adaptive_filters
Kosovar electrical engineer, linguist and academic
engagement with the Kosova Academy of Sciences and Arts as part of its Lexicographic Encyclopedic Centre, reflecting his interdisciplinary involvement beyond
Nebi_Caka
Partial order between random variables
Dentcheva, D.; Ruszczyński, A. (2003). "Optimization with Stochastic Dominance Constraints". SIAM Journal on Optimization. 14 (2): 548–566. CiteSeerX 10.1.1
Stochastic_dominance
problem is also CC-complete. Another problem which is CC-complete is lexicographically-first maximal matching. In this problem, we are given a bipartite
CC_(complexity)
Multilingual neural machine translation service
Dictionary. (English database designed and developed for Foras na Gaeilge by Lexicography MasterClass Ltd.) Welsh language data from Gweiadur by Gwerin. Certain
Google_Translate
frequently used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the efficiency of other algorithms (such
Glossary_of_computer_science
Arabic–English dictionary
al-Zabidi which was completed in the early 19th century. In total, 112 lexicographic sources are cited in the work. The lexicon was designed to consist of
Arabic–English_Lexicon
String-searching algorithm
alphabet, it can be computed in 2m comparisons, by computing the lexicographically larger of two ordered maximal suffixes, defined for order ≤ and ≥
Two-way string-matching algorithm
Two-way_string-matching_algorithm
machine-readable dictionaries. It is distinguished from computational lexicography, which more properly would be the use of computers in the construction
Computational_lexicology
Dictionary with data in digital form
exploited. Two advantages are that limitations of space (and the need to optimize its use) become less pressing, so additional content can be provided; and
Electronic_dictionary
Computer network management and monitoring protocol
and their values. Returns a Response with variable binding for the lexicographically next variable in the MIB. The entire MIB of an agent can be walked
Simple Network Management Protocol
Simple_Network_Management_Protocol
Binary representation for signed numbers
branch instructions. Unsigned binary numbers can be ordered by a simple lexicographic ordering, where the bit value 0 is defined as less than the bit value
Two's_complement
theory glossary. See also inequality, extreme value and mathematical optimization. Partially ordered set Preorder Totally ordered set Total preorder Chain
List_of_order_theory_topics
an LP-type problem (also called a generalized linear program) is an optimization problem that shares certain properties with low-dimensional linear programs
LP-type_problem
Arrangement of keys on a typographic keyboard
traditional Chinese characters. The bopomofo style keyboards are in lexicographic order, from top to bottom and left to right. The codes of three input
Keyboard_layout
Collection of subsets covering all t-element subsets
and Sloane for constructing lexicographic codes. The list of k {\displaystyle k} -subsets may be arranged in lexicographic order, colexicographic order
Covering_design
Typewriter that can type Chinese script
the system Lin devised for his Chinese-language dictionary, which lexicographically orders characters using thirty geometric shapes or strokes as tokens
Chinese_typewriter
Problem of allocation of money by consumers in order to most benefit themselves
represented by a continuous utility function. We will show that the lexicographic preference relation does not exhibits continuity: The consumer prefers
Utility_maximization_problem
2014 version of the Bible
bring the translation up to par with where textual criticism and Greek lexicography currently stand, not to mention alert Adam to a few all-out mistranslations
Bibliotheca_(Bible)
Composite data type
languages may also allow order comparisons ('<'and '>'), using the lexicographic order based on the comparison of individual fields.[citation needed]
Record_(computer_science)
Sequence of characters, data type
total order on Σ ∗ {\displaystyle \Sigma ^{*}} called lexicographical order. The lexicographical order is total if the alphabetical order is, but is not
String_(computer_science)
Pair of positions in a sequence where two elements are out of sorted order
permutations reverse colexicographic, and the right inversion count gives the lexicographic index. Inversion vector v {\displaystyle v} : With the element-based
Inversion (discrete mathematics)
Inversion_(discrete_mathematics)
Data about other data
because of exploitation of metadata and the practice of search engine optimization, SEO, to improve rankings. See the Meta element article for further discussion
Metadata
Problem in computer science and operations research
problem to an optimization problem, in which the loss function is a function describing the amount of envy. In general, this optimization problem is NP-hard
Envy_minimization
Branch of mathematics
(Better) (Pre) Well-order Constructions Composition Converse/Transpose Lexicographic order Linear extension Product order Reflexive closure Series-parallel
Order_theory
Linguistic model of well-formedness
64, 381–391. Tesar, Bruce. (2007). "A comparison of lexicographic and linear numeric optimization using violation difference ratios." Rutgers University
Harmonic_grammar
Mathematical construct in computer algebra
this two variable example, the monomial ordering that is used is the lexicographic order with x > y , {\displaystyle x>y,} and we consider the reduction
Gröbner_basis
Mathematical relation making a non-equal comparison
MR 2147066. Zbl 1091.26008. Ehrgott, Matthias (2005). Multicriteria Optimization. Springer-Berlin. ISBN 3-540-21398-8. Steele, J. Michael (2004). The
Inequality_(mathematics)
Variation to BCD-code where three (11) is added to a binary representation
New York, USA: van Nostrand. p. 182. Kautz, William H. (June 1954). "Optimized Data Encoding for Digital Computers". Convention Record of the I.R.E.
Excess-3
Roots of multiple multivariate polynomials
first the Gröbner basis for the graded reverse lexicographic order (grevlex), then deducing the lexicographical Gröbner basis by FGLM algorithm and finally
System of polynomial equations
System_of_polynomial_equations
Independent set which is not a subset of any other independent set
lower (i.e. has fewer neighbours). Break ties arbitrarily, e.g. using a lexicographic order on the vertex names. Add the set S to I. Remove from V the set
Maximal_independent_set
Software library for the C++ programming language
internally and other "diet template" techniques) and improving compilers' optimization techniques. However, this symptom is similar to naively manually copying
Standard_Template_Library
Task of computing complete subgraphs
are equal. As well as the problem of optimizing the sum of weights, other more complicated bicriterion optimization problems have also been studied. In
Clique_problem
Imitate-the-successful heuristic Plurality vote-based lexicographic heuristic Social heuristics Ecological rationality Optimization Risk Uncertainty Max Planck Institute
Social_rationality
Abbreviation consisting of initial letters of a phrase
stands for "HyperText Transfer Protocol" POWER stands for "Performance Optimization With Enhanced RISC", in which "RISC" stands for "reduced instruction
Acronym
Concept in economics and decision theory
preferences not to be representable by a utility function. An example is lexicographic preferences which are not continuous and cannot be represented by a
Utility
Methodic assignment of colors to elements of a graph
execution time of the resulting code, one of the techniques of compiler optimization is register allocation, where the most frequently used values of the
Graph_coloring
Dictionary of Modern Greek
ανάγκες) About the book [this book] is a landmark in Greek linguistics and lexicography. It provides the largest scale picture of the Greek language after the
Babiniotis_Dictionary
Municipality and largest city in China
the "14th Five-Year Plan for Ecological Space Construction and Amenity Optimization in Shanghai"] (PDF) (in Chinese). Shanghai Landscaping & City Appearance
Shanghai
Graph where every connected induced subgraph has a universal vertex
linear time algorithm for recognizing trivially perfect graphs, based on lexicographic breadth-first search. Whenever the LexBFS algorithm removes a vertex
Trivially_perfect_graph
Problem of finding the longest simple path for a given graph
O(n^{4})} . The latter algorithm is based on special properties of the lexicographic depth first search (LDFS) vertex ordering of co-comparability graphs
Longest_path_problem
Rule in social choice theory: choose the alternative maximizing the product of utilities
{\displaystyle p\to -\infty } gives the egalitarian rule (refined by lexicographic max-min optimization); and the limit p → 0 {\displaystyle p\to 0} gives the Nash
Nash_welfare_rule
Quickly growing function
each case the pair ( m , n ) {\displaystyle (m,n)} decreases in the lexicographic order on pairs, which is a well-ordering, just like the ordering of
Ackermann_function
Matrix in which most of the elements are zero
matrix in random order, but poor for iterating over non-zero values in lexicographical order. One typically constructs a matrix in this format and then converts
Sparse_matrix
Ability of artificial intelligence to play different games
Murphy, Tom (2013). "The First Level of Super Mario Bros. is Easy with Lexicographic Orderings and Time Travel ... after that it gets a little tricky." (PDF)
General_game_playing
{\displaystyle y_{i}} . It has been widely noted that the original lexicographic ordering based on coordinates when S {\displaystyle {\mathcal {S}}}
Vecchia_approximation
Chinese characters used in modern languages
or Chinese character optimization (漢字整理; 汉字整理; hànzì zhěnglǐ) is to, in addition to Chinese character simplification, optimize the Chinese characters
Modern_Chinese_characters
Web platform for language revitalization projects
Retrieved 21 February 2024. "FirstVoices — Introduction". Relational Lexicography. University of British Columbia. Retrieved 21 February 2024. "FirstVoices
FirstVoices
General purpose C++ library
MongoDB replica set support, C++ modules, ULID (universally unique lexicographically sortable identifier) support, and moving the minimum version to C++20
POCO_C++_Libraries
Algorithmic process of solving equations
equally long terms are ordered lexicographically. For a set T of terms, its disagreement path p is the lexicographically least path where two member terms
Unification (computer science)
Unification_(computer_science)
Database indexing technique
example, PostgreSQL versions 8.1 and later implement a "bitmap index scan" optimization to speed up arbitrarily complex logical operations between available
Bitmap_index
Set whose pairs have minima and maxima
Lattice Miner (theory and tool) Bloom filter Information flow Ordinal optimization Quantum logic Median graph Knowledge space Regular language learning
Lattice_(order)
radix quicksort algorithm sorts an array of N (pointers to) strings in lexicographic order. It is assumed that all strings are of equal length K; if the
Multi-key_quicksort
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