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Everything about Nonlinear programming
Solution process for some optimization problems
In mathematics, nonlinear programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Nonlinear programmingA 5-minute orientation
- Skim a recent paper: Two-Timescale Multilayer Recurrent Neural Networks for Nonlinear ProgrammingInfluential work since 2022
- Pick up a classic book: Nonlinear programmingThe most-reprinted book on the subject
- Read the landmark paper: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programmingCited 8,521 times
- Go sideways: Convex optimizationA closely related topic
- Go sideways: Mathematical optimizationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
On Nonlinear Fractional Programming
Nonlinear Programming
Nonlinear Programming
Nonlinear programming without computation
Stability in Nonlinear Programming
Nonlinear leastpth optimization and nonlinear programming
On parametric nonlinear programming
🆕 Influential since 2022
Two-Timescale Multilayer Recurrent Neural Networks for Nonlinear Programming
Programming nonlinear propagation for efficient optical learning machines
Nonlinear programming reformulation of dynamic flux balance analysis models
Convergence of augmented Lagrangian methods in extensions beyond nonlinear programming
Evolution-Guided Adaptive Dynamic Programming for Nonlinear Optimal Control
📚 Books worth reading
Nonlinear programmingM. S. Bazaraa · 1979- 📕Nonlinear programmingMokhtar S. Bazaraa, M.S. Bazaraa · 1993
Measurement error in nonlinear modelsRaymond J. Carroll, David Ruppert · 1995- 📕Non-Linear ProgrammingNita H. Shah, Poonam Prakash Mishra · 2020
Studies in linear and non-linear programmingKenneth Joseph Arrow, Kenneth J. Arrow · 1958
Nonlinear Time Series AnalysisThomas Schreiber · 1999
Linear and nonlinear rotordynamicsToshio Yamamoto, Yamamoto, Toshio · 2001
Integer programmingJohn K. Karlof · 2005
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Convex optimization Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently…
- Mathematical optimization Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria…
- Penalty method In mathematical optimization, penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces…
- Active-set method In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active…
- 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…
- Sequential quadratic programming Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization, also known as Lagrange-Newton method. SQP methods…
- Quadratic programming Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks…
- Constrained optimization In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function…