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Everything about Convex optimization
Subfield of mathematical optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets. Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Convex optimizationA 5-minute orientation
- Skim a recent paper: Non-convex sparse regularization via convex optimization for impact force identificationInfluential work since 2022
- Pick up a classic book: Convex optimization in signal processing and communicationsThe most-reprinted book on the subject
- Read the landmark paper: Exact Matrix Completion via Convex OptimizationCited 3,543 times
- Go sideways: Subgradient methodA closely related topic
- Go sideways: Nonlinear programmingA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Exact Matrix Completion via Convex Optimization
Robust Convex Optimization
Distributionally Robust Convex Optimization
Convex Optimization-Based Beamforming
Optimization of Convex Risk Functions
Structured Sparsity through Convex Optimization
Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
Convex two-level optimization
🆕 Influential since 2022
Non-convex sparse regularization via convex optimization for impact force identification
Non-convex sparse regularization via convex optimization for blade tip timing
Non-convex scenario optimization
Nesterov's Method for Convex Optimization
Temporal Logic Motion Planning With Convex Optimization via Graphs of Convex Sets
📚 Books worth reading
Convex optimization in signal processing and communicationsDaniel P. Palomar, Yonina C. Eldar · 2009
Geometric methods and optimization problemsV. G. Bolti͡anskiĭ, V. Boltyanski · 1998
Non-connected convexities and applicationsGabriela Cristescu, G. Cristescu · 2002
Variational Calculus and Optimal ControlJohn L. Troutman · 1995
Convex analysis and its applicationsA. Auslender · 1977
Convex functionsJonathan M. Borwein · 2010
Abstract convex analysisIvan Singer · 1997
Optimization ModelsGiuseppe C. Calafiore, Laurent El Ghaoui · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Subgradient method Subgradient methods are convex optimization methods which use subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s, subgradien…
- Nonlinear programming In mathematics, nonlinear programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the…
- Mathematical optimization Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria…
- Lagrangian relaxation In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization…
- Convex analysis Convex analysis is the branch of mathematics that studies convex sets, convex functions, and their applications to optimization, functional analysis, variationa…
- Penalty method In mathematical optimization, penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces…
- Interior-point method Interior-point methods (also referred to as barrier methods or IPMs) are algorithms for solving linear and non-linear convex optimization problems. IPMs…
- Duality (optimization) In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives…