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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 algorithms using quantum computing
(1997). "An exact duality theory for semidefinite programming and its complexity implications". Mathematical Programming. 77: 129–162. doi:10.1007/BF02614433
Quantum optimization algorithms
Quantum_optimization_algorithms
Subfield of convex optimization
known classes of convex optimization problems, namely linear and semidefinite programming. Given a real vector space X, a convex, real-valued function f
Conic_optimization
Optimization problem in mathematics
(2019-02-04). "Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs". Mathematical Programming. 181: 1–17. arXiv:1802
Quadratically constrained quadratic program
Quadratically_constrained_quadratic_program
Convex optimization problem
point methods and in general, can be solved more efficiently than semidefinite programming (SDP) problems. Some engineering applications of SOCP include filter
Second-order_cone_programming
Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to perform non-linear dimensionality
Semidefinite_embedding
Term in quantum information theory
channels. Although the diamond norm can be efficiently computed via semidefinite programming, it is in general difficult to obtain analytical expressions and
Diamond_norm
Geometric concept
Mittelmann, Hans D.; Vallentin, Frank (2010). "High accuracy semidefinite programming bounds for kissing numbers". Experimental Mathematics. 19 (2):
Kissing_number
Property of a mathematical matrix
^{\mathsf {T}}N\mathbf {x} \geq 0.} This property guarantees that semidefinite programming problems converge to a globally optimal solution. The positive-definiteness
Definite_matrix
Algorithms for solving convex optimization problems
O((k+m)1/2[mk2+k3+n3]). Interior point methods can be used to solve semidefinite programs. Affine scaling Augmented Lagrangian method Chambolle-Pock algorithm
Interior-point_method
Statistical analysis technique
penalized matrix decomposition framework, a convex relaxation/semidefinite programming framework, a generalized power method framework an alternating
Sparse_PCA
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
Numerical optimization process
sum-of-squares optimization is also known as the Lasserre hierarchy of semidefinite programming relaxations. Sum-of-squares optimization techniques have been applied
Sum-of-squares_optimization
Problem in computer science
Goemans, Michel X. (1997-10-01). "Semidefinite programming in combinatorial optimization". Mathematical Programming. 79 (1): 143–161. doi:10.1007/BF02614315
Square-root_sum_problem
Quantum
bounds on it, based on some given operator expectation values using semidefinite programming. The approach considers an optimization of the two-copy space.
Quantum_Fisher_information
Russian mathematician
optimization problems, and the first to make a systematic study of semidefinite programming (SDP). Also in this book, they introduced the self-concordant functions
Yurii_Nesterov
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
Method to solve optimization problems
Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique
Linear_programming
Partition of a graph's nodes into 2 disjoint subsets
approximation ratio using semidefinite programming. Note that min-cut and max-cut are not dual problems in the linear programming sense, even though one
Cut_(graph_theory)
ability to transform problems of polynomial optimization into semidefinite programming problems, which can be efficiently solved using convex optimization
Positive_polynomial
Matrix of inner products of vectors
L. E.; Jordan, M. I. (2004). Learning the kernel matrix with semidefinite programming. Journal of Machine Learning Research (Report). Vol. 5. pp. 27–72
Gram_matrix
Upper bound on a graph's Shannon capacity
approximations to this number can be computed in polynomial time by semidefinite programming and the ellipsoid method. The Lovász number of the complement of
Lovász_number
Mathematical convex optimization
Nemirovski. Semidefinite programming Spectrahedron Finsler's lemma Y. Nesterov and A. Nemirovsky, Interior Point Polynomial Methods in Convex Programming. SIAM
Linear_matrix_inequality
Shape that can be represented as a linear matrix inequality
Ramana, Motakuri; Goldman, A. J. (1995), "Some geometric results in semidefinite programming", Journal of Global Optimization, 7 (1): 33–50, CiteSeerX 10.1
Spectrahedron
Projection of data onto lower-dimensional manifolds
technique for casting this problem as a semidefinite programming problem. Unfortunately, semidefinite programming solvers have a high computational cost
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Theorem in functional analysis
C} is an absolute constant. This approximation algorithm uses semidefinite programming. We give a sketch of this approximation algorithm. Let B = ( b
Grothendieck_inequality
Mathematical optimization concept
(optimization) Semidefinite programming Relaxation (approximation) Gärtner, Bernd; Matoušek, Jiří (2006). Understanding and Using Linear Programming. Berlin:
Dual_linear_program
Process of reducing the number of random variables under consideration
instead of defining a fixed kernel, try to learn the kernel using semidefinite programming. The most prominent example of such a technique is maximum variance
Dimensionality_reduction
Method of data analysis
proposed, including a regression framework, a convex relaxation/semidefinite programming framework, a generalized power method framework an alternating
Principal_component_analysis
Vector quantization algorithm minimizing the sum of squared deviations
global optimization algorithms based on branch-and-bound and semidefinite programming have produced ‘’provenly optimal’’ solutions for datasets with
K-means_clustering
Problem in graph theory
approximation algorithms for maximum cut and satisfiability problems using semidefinite programming", Journal of the ACM, 42 (6): 1115–1145, doi:10.1145/227683.227684
Maximum_cut
Applied Mathematician
Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints", Mathematical Programming Computation Vol. 7, Issue 3 (2015)
Defeng_Sun
Unsolved problem in computational complexity theory
problem the best approximation ratio is given by a certain simple semidefinite programming instance, which is in particular polynomial. In 2010, Prasad Raghavendra
Unique_games_conjecture
Matrix decomposition method
IEEE. pp. 70–72. arXiv:1111.4144. So, Anthony Man-Cho (2007). A Semidefinite Programming Approach to the Graph Realization Problem: Theory, Applications
Cholesky_decomposition
Singaporean mathematician
and application of convex optimization, especially semidefinite programming and conic programming. Toh received BSc (Hon.) in 1990 and MSc in 1992, from
Kim-Chuan_Toh
Scientific study of digital information
(January 2018). "LQG Control With Minimum Directed Information: Semidefinite Programming Approach". IEEE Transactions on Automatic Control. 63 (1): 37–52
Information_theory
Graph with tight clique-coloring relation
The solution method for semidefinite programs, used by this algorithm, is based on the ellipsoid method for linear programming. It leads to a polynomial
Perfect_graph
On domino tiling after removing two corners
formulating it as a constraint satisfaction problem, and applying semidefinite programming to a relaxation. In 1964, John McCarthy proposed the mutilated
Mutilated_chessboard_problem
Mathematic definition
extension complexity has also been generalized from linear programming to semidefinite programming, by considering projections of spectrahedra in place of
Extension_complexity
Study of mathematical algorithms for optimization problems
Second-order cone programming (SOCP) is a convex program, and includes certain types of quadratic programs. Semidefinite programming (SDP) is a subfield
Mathematical_optimization
Bound on probability of a random variable being far from its mean
; Comanor, K. (2007-01-01). "Generalized Chebyshev Bounds via Semidefinite Programming". SIAM Review. 49 (1): 52–64. Bibcode:2007SIAMR..49...52V. CiteSeerX 10
Chebyshev's_inequality
Optimization software package
solves conic quadratic (a.k.a. Second-order cone programming) and semi-definite (aka. semidefinite programming) problems. A special feature of the solver,
MOSEK
Algebraic modeling language
constraints Mixed-integer nonlinear programming Second-order cone programming Global optimization Semidefinite programming problems with bilinear matrix inequalities
AMPL
Type of matrix
p. 299. ISBN 978-0-387-70872-0. So, Anthony Man-Cho (2007). A Semidefinite Programming Approach to the Graph Realization Problem: Theory, Applications
Euclidean_distance_matrix
French mathematician
her work in coding theory, kissing numbers, lattice theory, and semidefinite programming. She is a professor of mathematics at the University of Bordeaux
Christine_Bachoc
Task of computing complete subgraphs
maximum clique in polynomial time, using an algorithm based on semidefinite programming. However, this method is complex and non-combinatorial, and specialized
Clique_problem
Czech mathematician (1963–2015)
Society, 2010, ISBN 978-0-8218-4977-4. Approximation Algorithms and Semidefinite Programming (with B. Gärtner). Springer Berlin Heidelberg, 2012, ISBN 978-3-642-22014-2
Jiří_Matoušek_(mathematician)
Topics referred to by the same term
level mode of certain generations of Intel's mobile processors Semidefinite programming, an optimization procedure Service data point, a node in mobile
SDP
Generalization of the ellipse to allow more than two foci
Papers of James Clerk Maxwell: 1846-1862 P.L. Rosin: "On the Construction of Ovals" B. Sturmfels: "The Geometry of Semidefinite Programming", pp. 9–16.
N-ellipse
Algorithmic technique using hashing
approximation algorithms for maximum cut and satisfiability problems using semidefinite programming". Journal of the ACM. 42 (6). Association for Computing Machinery
Locality-sensitive_hashing
Algorithm that estimates unknowns from a series of measurements over time
(2009). "Estimation of the disturbance structure from data using semidefinite programming and optimal weighting". Automatica. 45 (1): 142–148. Bibcode:2009Autom
Kalman_filter
File format for presenting and archiving mathematical programming problems
constraints Mixed-integer nonlinear programming Second-order cone programming Global optimization Semidefinite programming problems with bilinear matrix inequalities
Nl_(format)
Graph used in computational complexity theory and graph theory
computational complexity theorists, as difficult examples for semidefinite programming based approximation algorithms for the vertex cover and graph coloring
Frankl–Rödl_graph
Proposed design of bank notes
published in 1983. A formal proof of security, using techniques from semidefinite programming, was given in 2013.In addition to a unique serial number on each
Quantum_money
Theoretical upper limit to non-local correlations in quantum mechanics
computational method for upperbounding it is a convergent hierarchy of semidefinite programs, the NPA hierarchy, that in general does not halt. The exact values
Tsirelson's_bound
Methodic assignment of colors to elements of a graph
coloring of perfect graphs can be computed in polynomial time using semidefinite programming. Closed formulas for chromatic polynomials are known for many classes
Graph_coloring
Technique in graph theory
graph homomorphism inequalities with computers by reducing them to semidefinite programming problems. Originally introduced by Alexander Razborov in a 2007
Flag_algebra
Czech mathematician (1951–1995)
graph theory, convex and polyhedral relaxations, semidefinite programming, and other integer programming-related problems. His early work also included
Svatopluk_Poljak
in polynomial-time, it follows that QRG ⊆ EXP. Min-max theorem Semidefinite programming QIP (complexity) Gutoski, G; Watrous, J (2007). "Toward a general
Quantum_refereed_game
Statistical machine learning algorithm for metric learning
for k-nearest neighbor classification. The algorithm is based on semidefinite programming, a sub-class of convex optimization. The goal of supervised learning
Large_margin_nearest_neighbor
Deviations from local realism
correlations that is closed under wirings and can be characterized via semidefinite programming. It contains all correlations in Q c ⊃ Q ¯ {\displaystyle Q_{c}\supset
Quantum_nonlocality
Experimental technology level
graphs, QAOA at depth p=11 has been shown to outperform standard semidefinite programming algorithms. Even more remarkably, QAOA can exploit non-adiabatic
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Awarded every year by the American Mathematical Society
approximation algorithms for maximum cut and satisfiability problems using semidefinite programming". Journal of the ACM. 42 (6): 1115–1145. doi:10.1145/227683.227684
Leroy_P._Steele_Prize
Technique in numerical linear algebra
applications, including to recover a good solution from an inexact (semidefinite programming) relaxation. If additional constraint g ( p ^ ) ≤ 0 {\displaystyle
Low-rank_approximation
Search algorithm finding the position of a target value within a sorted array
(2007). "Quantum algorithms for the ordered search problem via semidefinite programming". Physical Review A. 75 (3). 032335. arXiv:quant-ph/0608161. Bibcode:2007PhRvA
Binary_search
Binary operation on graphs
doi:10.1016/j.jctb.2015.12.009. Bačík, R.; Mahajan, S. (1995). "Semidefinite programming and its applications to NP problems". Computing and Combinatorics
Graph_product
Hypothesis in computational complexity theory
referred to as UG-hard. In particular, assuming UGC there is a semidefinite programming algorithm that achieves optimal approximation guarantees for many
Computational hardness assumption
Computational_hardness_assumption
Belgian-American mathematician
Fulkerson Prize for joint work with David P. Williamson on the semidefinite programming approximation algorithm for the maximum cut problem. In 2012 Goemans
Michel_Goemans
Elementwise product of two matrices
D)=(AC)\odot (BD).} The Hadamard product of two positive-semidefinite matrices is positive-semidefinite. This is known as the Schur product theorem, after Russian
Hadamard_product_(matrices)
Measurement in quantum metrology
optimization in quantum metrology and entanglement theory using semidefinite programming". Quantum Science and Technology. 11 (1): 015042. doi:10.1088/2058-9565/ae24a6
Quantum_metrological_gain
Logic problem, AND of pairwise ORs
second, in a graph related to the implication graph, and applying semidefinite programming methods to this cut problem, it is possible to find in polynomial
2-satisfiability
Overview of and topical guide to statistics
Linear programming Linear matrix inequality Quadratic programming Quadratically constrained quadratic program Second-order cone programming Semidefinite programming
Outline_of_statistics
Quantum-informatics technique
explicit form in the general case, it can be solved numerically via Semidefinite programming. An alternative approach to discriminate between a given ensemble
Quantum_state_discrimination
Mathematics term
solving a noncommutative analog of the sum of squares hierarchy of semidefinite programming problems numerically on a computer. Notably, this method has confirmed
Kazhdan's_property_(T)
Concept in network science
Successful algorithms include spectral clustering of the vertices, semidefinite programming, forms of belief propagation, and community detection among others
Stochastic_block_model
Award for advancements in discrete mathematics
and David P. Williamson for approximation algorithms based on semidefinite programming. Michele Conforti, Gérard Cornuéjols, and M. R. Rao for recognizing
Fulkerson_Prize
Russian and Israelian mathematician
optimization problems, and the first to make a systematic study of semidefinite programming (SDP). Also in this book, they introduced the self-concordant functions
Arkadi_Nemirovski
Mathematics of convex functions and sets
provides certificates of optimality. Linear programming, quadratic programming, semidefinite programming, and many methods in statistics and machine learning
Convex_analysis
Programming language
JuMP supports linear programming, mixed integer programming, semidefinite programming, conic optimization, nonlinear programming, and other classes of
JuMP
American computer scientist
for semidefinite programming, SIAM Journal on Optimization, 6:342–361, 1996. Vanderbei, R.J.: LOQO: An interior point code for quadratic programming, Optimization
Robert_J._Vanderbei
Zwick presented the algorithm in 1997. The algorithm is based on semidefinite programming. It can be derandomized using, e.g., the techniques from to yield
Karloff–Zwick_algorithm
Indian-American computer scientist
Raghavendra showed that assuming the unique games conjecture, semidefinite programming is the optimal algorithm for solving constraint satisfaction problems
Prasad_Raghavendra
Node labeling problem in graph theory
n ) {\displaystyle O(\log ^{3}n{\sqrt {\log \log n}})} , using semidefinite programming. For the case of dense graphs, a 3-approximation algorithm is known
Graph_bandwidth
Geometrical structure
obtained using a continuous analog of the sum of squares hierarchy of semidefinite programs. In many chemical situations such as ionic crystals, the stoichiometry
Sphere_packing
All curves of constant width have the same perimeter
doi:10.1007/BF02413320. Bayen, Térence; Henrion, Didier (2012), "Semidefinite programming for optimizing convex bodies under width constraints", Optimization
Barbier's_theorem
and chromatic number that can be computed in polynomial time by semidefinite programming. Thomsen graph The Thomsen graph is a name for the complete bipartite
Glossary_of_graph_theory
Java math library
Second Order Conic Programming SDP - Explanation of Semidefinite Programming SQP - Explanation of Sequential quadratic programming Interior Point Method
SuanShu_numerical_library
Mathematical method to constrain and solve conformal field theories
1007/s10955-014-1042-7. S2CID 39692193. Simmons-Duffin, David (2015). "A semidefinite program solver for the conformal bootstrap". Journal of High Energy Physics
Conformal_bootstrap
Mathematical set closed under positive linear combinations
and the Loewner order on positive semidefinite matrices. Such an ordering is commonly found in semidefinite programming. Cone (disambiguation) Cone (geometry)
Convex_cone
American computer scientist
Linear and Nonlinear Programming. In recent years, Ye has developed computational methods and theory using semidefinite programming for practical problems
Yinyu_Ye
Measure of unpredictability of outcomes
\|_{\rm {op}},} remembering that the operator norm of a Hermitian positive semidefinite operator equals its largest eigenvalue. Let ρ A B {\displaystyle \rho
Min-entropy
Canadian computer scientist (1968–2010)
He proved with his coauthors essentially that a huge class of semidefinite programming algorithms for the famous vertex cover problem will not achieve
Avner_Magen
Navigation and surveillance technique
solutions of time difference of arrival source localization based on semidefinite programming and Lagrange multiplier: complexity and performance analysis,"
Pseudo-range_multilateration
Solvability theorem for finite systems of linear inequalities
linear programming duality and has played a central role in the development of mathematical optimization (alternatively, mathematical programming).[citation
Farkas'_lemma
American mathematician
for his work with Goemans on approximation algorithms based on semidefinite programming, for which they won the Fulkerson Prize in 2000. He also received
David_P._Williamson
Electrical and Electronics Engineers (IEEE) in 2016 for contributions to semidefinite and sum-of-squares optimization. He was named a SIAM Fellow in 2018.
Pablo_Parrilo
finite elements limit analysis for Hoek-Brown materials using semidefinite programming." Journal of Engineering Mechanics 143.9 (2017): 04017077.doi:10
Finite_element_limit_analysis
German computer scientist
Prasad; Steurer, David (June 2015). "Lower bounds on the size of semidefinite programming relaxations". STOC '15: Proceedings of the forty-seventh annual
David_Steurer
Filling in missing entries of a matrix
L0-norm for vectors. The convex relaxation can be solved using semidefinite programming (SDP) by noticing that the optimization problem is equivalent to
Matrix_completion
Samson (2022). "Learning-Augmented Algorithms for Online Linear and Semidefinite Programming". arXiv:2209.10614 [cs]. Im, Sungjin; Kumar, Ravi; Montazer Qaem
Learning_augmented_algorithm
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu, Traditional
One whose Eyes are Beautiful Like Lotuses
Boy/Male
Biblical American Hebrew
The strength of God.
Boy/Male
German
Graceful; Bright or Shining Intellect; Bright Mind
Girl/Female
Hindu, Indian, Marathi
Peak of Gold
Girl/Female
Muslim
Truly, Kind person, Beautiful
Boy/Male
Sikh
One whose mine is at peace, Peaceful heart mind, Soul
Boy/Male
Hindu, Indian
Surajiv
Boy/Male
Gujarati, Hindu, Indian, Kannada
Cutting
Boy/Male
Hindu
The monkey God of ramayana
Boy/Male
Sikh
Victory of charm, Enticing victor
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING
SEMIDEFINITE PROGRAMMING