A tutorial on geometric programming

By Stephen P. Boyd, Seung-Jean Kim, Lieven Vandenberghe, Arash Hassibi. Optimization and Engineering, 2007

1,250 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/1499f206b576914668ce4d01829f401ef57e4cf8

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Citations in the corpus

A Rewriting System for Convex Optimization Problems (2017, background): “For a brief introduction to geometric programming, see (Boyd & Vandenberghe, 2004, § 4.5); for a longer survey, see (Boyd, Kim, Vandenberghe, & Hassibi, 2007).”
Why Interpretability in Machine Learning? An Answer Using Distributed Detection and Data Fusion Theory (2018, neutral): “8 in Boyd et al. (2007).”
Cones and interior-point algorithms for structured convex optimization involving powers andexponentials (2009, background): “alpha = [p(end)/p(1);p(end)/p(2);1/p(end)*ones(2,1)]; K = struct(’f’,1,’l’,1,’p’,alpha,’e’,0,’pd’,’d’); b = sparse((1:3),ones(3,1),[-d;-1],7,1); c = sparse([2,4,7],[1,1,1],[1,1,1],14,1); A_f = sparse([3,6,7],ones(3,1),[-1,1,1],7,1); A_l = sparse(3,1,1,7,1); A_p = sparse([1,2,3,3,4,4,5,5,6,7],[3,6,8,”
Unifying Heterogeneous Classifiers With Distillation (2019, background): “Optimisation Minimisation of (7) can be transformed into a geometric program (see supplementary material), which can then be converted to a convex problem and efficiently solved [3].”
Convergent Propagation Algorithms via Oriented Trees (2007, background): “Here we argue that the function F D ( β ; ρ, θ ) is a convex function of β . the We ﬁrst deﬁne class of posynomial functions as functions of the form [9] f where c k > 0.”
Geometric Programming for Communication Systems (2005, background): “Detailed discussion of GP can be found in the following books, book chapters, and survey articles: [52, 133, 10, 6, 51, 103, 54, 20].”
The CVX Users' Guide (2015, methodology): “For background on geometric programming, see the tutorial paper [BKVH05], available at www.”
Power Control By Geometric Programming (2007, background): “The best local monomial approximation g̃(x0) of g(x0) near x0 can be easily verified [4].”
Cooperative Jamming for Secure Communications in MIMO Relay Networks (2011, methodology): “The GP problems in this successive optimization method can be solved using interior-point methods with polynomial-time complexity [36], and it has been proven in [35] that the solution obtained using successive approximations for the single condensation method will efficiently converge to a point sa”
Multivariate convex regression with adaptive partitioning (2011, methodology): “Key words: Nonparametric regression, shape constraint, convex regression, treed linear model, adaptive partitioning”
Sub-Channel Assignment, Power Allocation, and User Scheduling for Non-Orthogonal Multiple Access Networks (2016, methodology): “Given the sub-channel allocation, the power allocation problem can then be formulated as geometric programming (GP) [30], [31], i.e., a convex problem in which the global-optimal solution can be obtained via efﬁcient interior point methods [32].”
Binary Power Control for Sum Rate Maximization over Multiple Interfering Links (2008, methodology): “Hence, (22) is not a GP in standard form, but a signomial programming (SP) problem [14].”
First-order Methods for Geodesically Convex Optimization (2016, background): “At a more familiar level, implicitly the topic of “geometric programming” (Boyd et al., 2007) may be viewed as a special case of g-convex optimization (Sra and Hosseini, 2015).”