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Everything about Vector optimization
Vector optimization is a subarea of mathematical optimization where optimization problems with vector-valued objective functions are optimized with respect to a given partial ordering and subject to certain constraints. A multi-objective optimization problem is a special case of a vector optimization problem: The objective space is the finite dimensional Euclidean space partially ordered by the component-wise "less than or equal to" ordering. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Vector optimizationA 5-minute orientation
- Skim a recent paper: INFO: An efficient optimization algorithm based on weighted mean of vectorsInfluential work since 2022
- Pick up a classic book: Optimization by Vector Space MethodsThe most-reprinted book on the subject
- Read the landmark paper: Scalarizing vector optimization problemsCited 274 times
- Go sideways: Duality (optimization)A closely related topic
- Go sideways: Balanced setA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Scalarizing vector optimization problems
Proximal Methods in Vector Optimization
Super efficiency in vector optimization
Scalarization in vector optimization
Strict Efficiency in Vector Optimization
From Scalar to Vector Optimization
Improvement sets and vector optimization
Duality in vector optimization
🆕 Influential since 2022
INFO: An efficient optimization algorithm based on weighted mean of vectors
Nonlinear optimization and support vector machines
Four vector intelligent metaheuristic for data optimization
Spectral conjugate gradient methods for vector optimization problems
Conditional gradient method for vector optimization
📚 Books worth reading
Optimization by Vector Space MethodsDavid G. Luenberger, David G. Luenberger · 1968
Vector OptimizationJohannes Jahn · 2004
Mathematics for Machine LearningMarc Peter Deisenroth, A. Aldo Faisal · 2019
Set-valued OptimizationAkhtar A. Khan, Christiane Tammer · 2014
Quantitative Pareto analysis by cone separation techniqueIgnacy Kaliszewski · 1994
Variable Ordering Structures in Vector OptimizationGabriele Eichfelder · 2014
Recent developments in vector optimizationQamrul Hasan Ansari, Jen-Chih Yao · 2011
Duality in Vector OptimizationRadu Ioan Ioan Bot, Sorin-Mihai Grad · 2009
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 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…
- Balanced set In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space (over a field K {\displaystyle \mathbb {K} } with…
- Normal cone (variational analysis) In variational analysis, set-valued analysis and optimization, the concept of a normal cone to a subset of a space generalizes that of the orthogonal complement…
- Multi-objective linear programming Multi-objective linear programming is a subarea of mathematical optimization. A multiple objective linear program (MOLP) is a linear program with more…
- Perturbation function In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any…
- Absorbing set In functional analysis and related areas of mathematics an absorbing set in a vector space is a set S {\displaystyle S} which can be "inflated" or "scaled…
- Ellipsoid method In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates…
- Rademacher complexity In computational learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of…