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Vector optimization information


Vector optimization is a subarea of mathematical optimization where optimization problems with a 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.

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Vector optimization

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Vector optimization is a subarea of mathematical optimization where optimization problems with a vector-valued objective functions are optimized with respect...

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Test functions for optimization

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single-objective optimization cases are presented. In the second part, test functions with their respective Pareto fronts for multi-objective optimization problems...

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Hyperparameter optimization

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hyperparameter optimization methods. Bayesian optimization is a global optimization method for noisy black-box functions. Applied to hyperparameter optimization, Bayesian...

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Support vector machine

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In machine learning, support vector machines (SVMs, also support vector networks) are supervised max-margin models with associated learning algorithms...

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Sequential minimal optimization

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minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines...

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Vector database

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A vector database, vector store or vector search engine is a database that can store vectors (fixed-length lists of numbers) along with other data items...

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Particle swarm optimization

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by using another overlaying optimizer, a concept known as meta-optimization, or even fine-tuned during the optimization, e.g., by means of fuzzy logic...

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Mathematical optimization

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generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...

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Bilevel optimization

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Bilevel optimization is a special kind of optimization where one problem is embedded (nested) within another. The outer optimization task is commonly referred...

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Vectorization

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elements Automatic vectorization, a compiler optimization that transforms loops to vector operations Image tracing, the creation of vector from raster graphics...

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Convex optimization

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Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

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Harold Benson

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explore properly efficient solutions of nonlinear vector optimization problems. In global optimization, he focused a good portion of his work on the theory...

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Loop optimization

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representations of the computation being optimized and the optimization(s) being performed. Loop optimization can be viewed as the application of a sequence...

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Optimization problem

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science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided...

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Stochastic gradient descent

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already been introduced, and was added to SGD optimization techniques in 1986. However, these optimization techniques assumed constant hyperparameters,...

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Advanced Vector Extensions

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Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge New Instructions) are SIMD extensions to the x86 instruction...

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Automatic vectorization

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that can be vectorized, relying on the data dependence of the instructions inside loops. Automatic vectorization, like any loop optimization or other compile-time...

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Query optimization

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optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts...

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Vector Informatik

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Sweden, and the USA. Vector Informatik also includes Vector Consulting Services GmbH, a consultation firm specializing in optimization of technical product...

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Gradient descent

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Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for finding a local minimum of a differentiable...

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List of numerical analysis topics

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conflicting objectives Benson's algorithm — for linear vector optimization problems Bilevel optimization — studies problems in which one problem is embedded...

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Intel Advisor

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known as "Advisor XE", "Vectorization Advisor" or "Threading Advisor") is a design assistance and analysis tool for SIMD vectorization, threading, memory use...

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Lexicographic optimization

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Lexicographic optimization is a kind of Multi-objective optimization. In general, multi-objective optimization deals with optimization problems with two...

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Optimizing compiler

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use, storage size, and power consumption. Optimization is generally implemented as a sequence of optimizing transformations, algorithms that transform...

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Conic optimization

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Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine...

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