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Minimizing and maximizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint

Zofia Matusiewicz (2022)

Kybernetika

This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to max - * fuzzy relational equations and an inequality constraint, where * is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy max - * relational equation and an inequality constraint,...

Model selection for regression on a random design

Yannick Baraud (2002)

ESAIM: Probability and Statistics

We consider the problem of estimating an unknown regression function when the design is random with values in ℝ k . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small probability....

Model selection for regression on a random design

Yannick Baraud (2010)

ESAIM: Probability and Statistics

We consider the problem of estimating an unknown regression function when the design is random with values in ℝ k . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of small...

Nonlinear Rescaling Method and Self-concordant Functions

Richard Andrášik (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Nonlinear rescaling is a tool for solving large-scale nonlinear programming problems. The primal-dual nonlinear rescaling method was used to solve two quadratic programming problems with quadratic constraints. Based on the performance of primal-dual nonlinear rescaling method on testing problems, the conclusions about setting up the parameters are made. Next, the connection between nonlinear rescaling methods and self-concordant functions is discussed and modified logarithmic barrier function is...

On an optimization problem arising from probability density estimation.

Sankar Basu, Mohammad Saif Ullah Khan, C.A. Micchelli, Peder A. Olsen (2002)

RACSAM

Consideramos una clase de problemas de optimización que surgen en estimaciones de la densidad de datos en dimensión elevada a partir de proyecciones en subespacios de dimensión más baja. Los criterios que se usan para la selección óptima del modelo son máxima entropía y máxima verosimilitud. En cada caso nuestro planteamiento requiere estimadores de la densidad univariados y a este respecto exploramos el uso de modelos mezcla de densidades gaussianas y de estimadores de Parzen para los datos proyectados....

On complete-cocomplete subspaces of an inner product space

David Buhagiar, Emmanuel Chetcuti (2005)

Applications of Mathematics

In this note we give a measure-theoretic criterion for the completeness of an inner product space. We show that an inner product space S is complete if and only if there exists a σ -additive state on C ( S ) , the orthomodular poset of complete-cocomplete subspaces of S . We then consider the problem of whether every state on E ( S ) , the class of splitting subspaces of S , can be extended to a Hilbertian state on E ( S ¯ ) ; we show that for the dense hyperplane S (of a separable Hilbert space) constructed by P. Pták and...

On cyclic α(·)-monotone multifunctions

S. Rolewicz (2000)

Studia Mathematica

Let (X,d) be a metric space. Let Φ be a linear family of real-valued functions defined on X. Let Γ : X → 2 Φ be a maximal cyclic α(·)-monotone multifunction with non-empty values. We give a sufficient condition on α(·) and Φ for the following generalization of the Rockafellar theorem to hold. There is a function f on X, weakly Φ-convex with modulus α(·), such that Γ is the weak Φ-subdifferential of f with modulus α(·), Γ ( x ) = ∂ Φ - α f | x .

Currently displaying 161 – 180 of 348