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Theoretical Aspect of Diagonal Bregman Proximal Methods
In this paper, we propose and study a diagonal inexact version of Bregman proximal methods, to solve convex optimization problems with and without constraints. The proposed method forms a unified framework for existing algorithms by providing others.
Computing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equations
In a previous paper, we have shown that forward use of the steady-state difference equations arising from homogeneous discrete-state space Markov chains may be subject to inherent numerical instability. More precisely, we have proven that, under some appropriate assumptions on the transition probability matrix P, the solution space S of the difference equation may be partitioned into two subspaces , where the stationary measure of P is an element of , and all solutions in are asymptotically dominated by the solutions corresponding to . In this paper, we discuss the analogous problem of computing hitting probabilities of Markov chains, which is affected by the same numerical phenomenon. In addition, we have to fulfill a somewhat complicated side condition which essentially differs from those conditions one is usually confronted with when solving initial and boundary value problems. To extract the desired solution, an efficient and numerically stable generalized-continued-fraction-based algorithm is developed.
Partial Derivative Estimation for Underlying Functional-Valued Process in a Unified Framework
We consider functional data analysis when the observations at each location are functional rather than scalar. When the dynamic of underlying functional-valued process at each location is of interest, it is desirable to recover partial derivatives of a sample function, especially from sparse and noise-contaminated measures. We propose a novel approach based on estimating derivatives of eigenfunctions of marginal kernels to obtain a representation for functional-valued process and its partial derivatives in a unified framework in which the number of locations and number of observations at each location for each individual can be any rate relative to the sample size. We derive almost sure rates of convergence for the procedures and further establish consistency results for recovered partial derivatives.
Some Hyperbolic Iterative Methods for Linear Systems
The indefinite inner product defined by , arises frequently in some applications, such as the theory of relativity and the research of the polarized light. This indefinite scalar product is referred to as hyperbolic inner product. In this paper, we introduce three indefinite iterative methods: indefinite Arnoldi’s method, indefinite Lanczos method (ILM), and indefinite full orthogonalization method (IFOM). The indefinite Arnoldi’s method is introduced as a process that constructs a J-orthonormal basis for the nondegenerated Krylov subspace. The ILM method is introduced as a special case of the indefinite Arnoldi’s method for J-Hermitian matrices. IFOM is mentioned as a process for solving linear systems of equations with J-Hermitian coefficient matrices. Finally, by providing numerical examples, the FOM, IFOM, and ILM processes have been compared with each other in terms of the required time for solving linear systems and also from the point of the number of iterations.
Predicting the Viscosity of Petroleum Emulsions Using Gene Expression Programming (GEP) and Response Surface Methodology (RSM)
This paper summarizes an investigation of certain operating parameters on the viscosity of petroleum emulsions. The production of crude oil is accompanied by emulsified water production, which comes along with various challenges like corroding the transport systems and catalysts poisoning during petroleum refining in the downstream. Several process variables are believed to affect the ease with which emulsified water can be separated from emulsions. Some of the issues have not been extensively examined in the literature. The simplicity with which water is separated from petroleum changes with age (after formation) of the emulsion; notwithstanding, this subject has not been investigated broadly in literature. This study tries to assess the correlation between aging time, water cut, crude oil viscosity, water viscosity and amount of solids and viscosity of petroleum emulsions. To achieve that, a response surface methodology (RSM) based on Box-Behnken design (BBD) was used to design the experiment. Synthetic emulsions were prepared from an Offshore Malaysian Crude oil based on the DoE design and were aged for 7 days. The emulsions viscosities were measured at 60-degree Celsius using an electromagnetic viscometer (EV100). The broad pressure and temperature range of the HPHT viscometer permit the imitation of acute conditions under which such emulsions may form. The data obtained from the RSM analysis was used to develop a prediction model using gene expression programming (GEP). It was discovered that the viscosity of water has no effect on the viscosities of the studied emulsions, as does the water cut and amount of solids. The most significant factor that affects emulsion viscosity is the aging time, with the emulsion becoming more viscous over time. This is believed to be imminent because of variations in the interfacial film structure. This is followed by the amount of solids, also believed to be as a result of increasing coverage at the interface of the water droplets, limiting the movements of the dispersed droplets (reduced coalescence), thereby increasing the viscosity of the emulsions.
Discretization of Optimal Control Problems Governed by p-Laplacian Elliptic Equations
In this paper, a state-constrained optimal control problem governed by p-Laplacian elliptic equations is studied. The feasible control set or the cost functional may be nonconvex, and the purpose is to obtain the convergence of a solution of the discretized control problem to an optimal control of the relaxed continuous problem.