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Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

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Overview

Definition

Special cases

Properties

Algorithms

Lagrange multipliers

Applications

Extensions

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Map overview Semantic statistics

Convex optimization

Nodes74
Edges73
Triples134
Avg. degree1.97
Density0.027027
Components1

How this topic connects Entity context

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Convex optimization

Top relations

related to References · 78
Convex optimization → Adrian, Advanced, An, Anders Klarbring, Angelia, Apr, Arkadii, Asuman, Athena Scientific, Belmont, Berlin, Bertsekas, Borwein, Business Media, Christensen, Claude, Computational, Computer Science, Convex, Convex Analysis
related to External links · 13
Convex optimization → An, Borchers, Boyd, Convex Analysis, Convex Optimization II, EE364a, EE364b, Lieven Vandenberghe, MIT OCW, Optimization, Optimization Book, Stanford, Stephen
related to Eliminating linear equality constraints · 11
Convex optimization → Ax, Denote, Fz, If Ax, In, It, Note, Otherwise, Rk, Substituting, This
has application · 10
Convex optimization → Combinatorial, Convex, Electricity, Localization, Model, Non-probabilistic, Optimal, Portfolio, Variations, Worst-case
related to Special cases · 8
Convex optimization → Conic, In LP, In QP, Linear, Quadratic, Second, Semidefinite, The
related to General problems · 5
Convex optimization → Convex, Phase, Such, The, They
related to Software · 5
Convex optimization → Modeling, Solvers, There, They, This
is a · 1
Convex optimization → subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets
related to Abstract form · 1
Convex optimization → The
related to Extensions · 1
Convex optimization → Extensions

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Important terminology

convex optimization problem problems constraints displaystyle objective analysis general isbn function methods linear equality algorithms form unconstrained set standard minimization

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Convex optimizationis asubfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets0.90text
Convex optimizationhas applicationConvex0.60section
Convex optimizationhas applicationPortfolio0.60section
Convex optimizationhas applicationWorst-case0.60section
Convex optimizationhas applicationOptimal0.60section
Convex optimizationhas applicationVariations0.60section
Convex optimizationhas applicationModel0.60section
Convex optimizationhas applicationElectricity0.60section
Convex optimizationhas applicationCombinatorial0.60section
Convex optimizationhas applicationNon-probabilistic0.60section
Convex optimizationhas applicationLocalization0.60section
Convex optimizationrelated to Abstract formThe0.60section

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