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Everything about Interior-point method
Algorithms for solving convex optimization problems
Interior-point methods are algorithms for solving linear and non-linear convex optimization problems. IPMs combine two advantages of previously-known algorithms:Theoretically, their run-time is polynomial—in contrast to the simplex method, which has exponential run-time in the worst case. Practically, they run as fast as the simplex method—in contrast to the ellipsoid method, which has polynomial run-time in theory but is very slow in practice. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Interior-point methodA 5-minute orientation
- Skim a recent paper: Robust Interior Point Method for Quantum Key Distribution Rate ComputationInfluential work since 2022
- Pick up a classic book: Arc-Search Techniques for Interior-point MethodsThe most-reprinted book on the subject
- Read the landmark paper: An Interior-Point Method for Semidefinite ProgrammingCited 542 times
- Go sideways: Ellipsoid methodA closely related topic
- Go sideways: Linear programmingA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
An Interior-Point Method for Semidefinite Programming
Improved interior point method for OPF problems
Interior-Point Method for Reservoir Operation with Stochastic Inflows
A Quantum Interior Point Method for LPs and SDPs
Inexact Interior-Point Method
An Interior-Point Method for a Class of Saddle-Point Problems
Matrix-free interior point method
Optimal reactive power control using modified interior point method
🆕 Influential since 2022
Robust Interior Point Method for Quantum Key Distribution Rate Computation
BELTISTOS: A robust interior point method for large-scale optimal power flow problems
An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization
A rate-independent crystal plasticity algorithm based on the interior point method
Sparse Approximations with Interior Point Methods
📚 Books worth reading
- 📕Arc-Search Techniques for Interior-point MethodsYaguang Yang · 2020
Interior point algorithmsYinyu Ye · 1997
Self-regularityJiming Peng · 2002
Interior point methods of mathematical programmingTamás Terlaky · 1996
Primal-dual interior-point methodsWright, Stephen J. · 1987
Interior Point Approach to Linear, Quadratic and Convex ProgrammingD. den Hertog · 1899
Interior point methods for linear optimizationCornelis Roos, Tamas Terlaky · 2005
Numerical optimizationJ. Frédéric Bonnans, Jean Charles Gilbert · 2003
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Ellipsoid method In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates…
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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…
- Karmarkar's algorithm Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient…
- Nonlinear programming In mathematics, nonlinear programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the…
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