Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy

Bucharest, Romania

Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy

Bucharest, Romania
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Stancu-Minasian I.M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy | Kummari K.,Indian School of Mines | Jayswal A.,Indian School of Mines
Numerical Functional Analysis and Optimization | Year: 2017

In this paper, we introduce the concept of higher-order (Φ, ρ)-V-invexity and present two types of higher-order dual models for a semi-infinite minimax fractional programming problem. Weak, strong, and strict converse duality theorems are discussed under the assumptions of higher-order (Φ, ρ)-V-invexity to establish a relation between the primal and dual problems. © 2017 Taylor & Francis.


Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy | Mininni R.M.,University of Bari | Romanelli S.,University of Bari
Journal of Optimization Theory and Applications | Year: 2017

We deal with an optimal control problem in coefficients for a strongly degenerate diffusion equation with interior degeneracy, which is due to the nonnegative diffusion coefficient vanishing with some rate at an interior point of a multi-dimensional space domain. The optimal controller is searched in the class of functions having essentially bounded partial derivatives. The existence of the state system and of the optimal control are proved in a functional framework constructed on weighted spaces. By an approximating control process, explicit approximating optimality conditions are deduced, and a representation theorem allows one to express the approximating optimal control as the solution to the eikonal equation. Under certain hypotheses, further properties of the approximating optimal control are proved, including uniqueness in some situations. The uniform convergence of a sequence of approximating controllers to the solution of the exact control problem is provided. The optimal controller is numerically constructed in a square domain. © 2017 Springer Science+Business Media New York


Jayswal A.,Indian School of Mines | Stancu-Minasian I.M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy | Choudhury S.,Indian School of Mines
OPSEARCH | Year: 2015

The aim of this paper is to introduce the concept of second-order (F, α, ρ, θ)-convexity for variational problems. An example is constructed to examine the existence of the introduced class of functions, which is more general than previously defined functions. In order to relate the primal variational problem and its second order dual, several duality results, viz., weak, strong and strict converse duality results are established. © 2014, Operational Research Society of India.


Preda V.,University of Bucharest | Preda V.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy | Dedu S.,University of Bucharest | Sheraz M.,Ningbo University
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2016

The aim of this paper is to develop some risk assessment models involving truncated and censored loss random variables. Representation formulas for the second order entropy corresponding to the left truncated or censored from below and right truncated or censored from above random variables are derived. Also, some properties and interpretations of the results are provided.


Beldiman M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2013

Some types of equilibrium problems and systems of equilibrium problems on cones are studied. For these, we obtain equivalence results and prove, using a fixed - point theorem of Chowdury and Tan, existence results.


Jayswa A.,Birla Institute of Technology | Stancu-Minasian I.M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2010

We introduce new classes of generalized convex n-set functions that we call d-weak strictly pseudoquasi type-I univex, d-strong pseudo-quasi type-I univex and d-weak strictly pseudo type-I univex functions. We focus on multiobjective subset programming problem. Sufficient optimality conditions are obtained under the assumptions involving such functions. Duality results are also established for Mond-Weir and general Mond-Weir type dual problems in which the functions involved satisfy appropriate generalized d-type-I univexity conditions. The results obtained in this paper present a refinement and improvement of previously known results in the literature.


Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy | Marinoschi G.,Simion Stoilow Institute of Mathematics of the Romanian Academy
Journal of Biological Dynamics | Year: 2013

We study a model, motivated by a bioremediation process, describing a cross-diffusion movement of a bacteria population b attracted by a chemoattractant signal c, in a nonhomogeneous stratified medium with n layers. We assume that this reaction-diffusion process is characterized by a low rate of degradation and a low diffusion coefficient of the chemoattractant, expressed in the model by a small parameter ε{lunate}. The model consists of n systems of nonlinear parabolic equations with transmission conditions between layers. We prove a global-in-time solution for the asymptotic model setup with respect to the small parameter of the problem, for arbitrarily large initial data. Next, we deal with the control problem focusing mainly on the reduction of the chemoattractant concentration, by acting upon the initial distribution of the bacteria population b0. To this end, we prove the existence of a solution to the control problem and determine the optimality conditions. © 2013 The Author(s). Published by Taylor & Francis.


Ionescu V.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science | Year: 2011

We give a new proof concerning the complete positivity of the Boolean product of contractive, completely positive maps between C*-Algebras (see [9]). This is inspired by a technique due to M. Bozejko, M. Leinert and R. Speicher from [6] and uses an extension of a W.L.Paschke and E. Stormer's criterion for the positivity of a matrix over a C*-Algebra[13] [18].


Barbu T.,Romanian Academy of Sciences | Marinoschi G.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
International Journal of Control | Year: 2016

We propose a technique for image denoising by solving a nonconvex optimal control problem with the state and controller connected on a manifold described by a nonlinear elliptic equation. The existence of a control able to denoise an initial blurred image is proved and the optimality conditions are determined by a passing to the limit technique in an appropriate approximating problem, involving the Legendre–Fenchel relations. An algorithm constructed on the basis of the theoretical results is developed and numerical simulations are provided. © 2016 Informa UK Limited, trading as Taylor & Francis Group


Popescu M.,Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
2011 International Conference on Communications, Computing and Control Applications, CCCA 2011 | Year: 2011

We consider the problem of optimum concerning to the minimization quadratic functionals of Bolza type with constraints represented differential systems with parameter. One demonstrates the uniqueness of optimal feedback nonlinear control obtained, by utilizing that the U Hilbert space control domain is rotund. The solution for two point boundary value problem implies the determination of the solution of the system in variations associated to the linearized system. The construction of the solution use of an iterative procedure, yielding the initial value results of the adjoint variable. By presenting the state vectors x X and the control vectors u U in orthonormal basis, one develops a numerical approximation method of the solution to the optimum problem. © 2011 IEEE.

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