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Everything about Constrained optimization
Optimizing objective functions that have constrained variables
In mathematical optimization, constrained optimization is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized. Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Constrained optimizationA 5-minute orientation
- Skim a recent paper: Geometrically Constrained Trajectory Optimization for MulticoptersInfluential work since 2022
- Pick up a classic book: Trends in PDE Constrained OptimizationThe most-reprinted book on the subject
- Read the landmark paper: An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box ConstraintsCited 6,964 times
- Go sideways: Differential evolutionA closely related topic
- Go sideways: Karush–Kuhn–Tucker conditionsA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints
A Limited Memory Algorithm for Bound Constrained Optimization
Teaching–learning-based optimization: A novel method for constrained mechanical design optimization problems
Energy-constrained modulation optimization
Stress constrained topology optimization
Distributed Asynchronous Constrained Stochastic Optimization
Blended biogeography-based optimization for constrained optimization
Slope constrained topology optimization
🆕 Influential since 2022
Geometrically Constrained Trajectory Optimization for Multicopters
A Survey on Evolutionary Constrained Multiobjective Optimization
An Evolutionary Multitasking Optimization Framework for Constrained Multiobjective Optimization Problems
A Multiform Optimization Framework for Constrained Multiobjective Optimization
Enhanced Remora Optimization Algorithm for Solving Constrained Engineering Optimization Problems
đź“š Books worth reading
Trends in PDE Constrained OptimizationGünter Leugering, Peter Benner · 2014
Practical Augmented Lagrangian Methods for Constrained OptimizationErnesto G. Birgin, JosĂ© Mario MartĂnez · 2014- đź“•Constrained Control of Uncertain, Time-Varying, Discrete-Time SystemsHoai-Nam Nguyen · 2013
Internal And External Stabilization Of Linear Systems With ConstraintsAli Saberi · 2012
Semismooth Newton methods for variational inequalities and constrained optimization problems in function spacesMichael Ulbrich · 2011
Constrained optimization and optimal control for partial differential equationsGünter Leugering · 2012
Feasibility and infeasibility in optimizationJ. W. Chinneck · 2008
Optimization of Objective FunctionsNinul Anatoly Sergeevich · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Differential evolution Differential evolution (DE) is an evolutionary algorithm to optimize a problem by iteratively trying to improve a candidate solution with regard to a given…
- Karush–Kuhn–Tucker conditions In mathematical optimization, the Karush–Kuhn–Tucker (KKT) conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes…
- Augmented Lagrangian method Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods…
- Penalty method In mathematical optimization, penalty methods are a certain class of algorithms for solving constrained optimization problems. A penalty method replaces…
- Constraint (mathematics) In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily…
- Simplex algorithm In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is an algorithm for linear programming. The name of the algorithm is derived…
- Multidisciplinary design optimization Multi-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of…
- 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…