Stationary phase point extraction based on high-resolution radon transform and its application to multiple attenuation by wavefield extrapolation

Multiple prediction and subtraction techniques based on wavefield extrapolation are effective for suppressing multiple related to water layers. In the conventional wavefield extrapolation method,the multiples of the seismic data are predicted from the known total wave field by the Green function convoluted with each point of the bottom. However,only the energy near the stationary phase point has an effect on the summation result when the convolutional gathers are added. The research proposed a stationary phase point extraction method based on high-resolution radon transform. In the radon domain,the energy near the stationary phase point is directly added along the convolutional gathers curve,which is a valid solution to the problem of the unstable phase of the events of multiple. The Curvelet matching subtraction technique is used to remove the multiple,which improved the accuracy of the multiple predicted by the wavefield extrapolation and the artifacts appearing around the events of multiple are well eliminated. The validity and feasibility of the proposed method are verified by the theoretical and practical data example.

Continuous feedback control of KdV Burgers system

The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationaxy points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment sepaxately.

A new smoothing technique for mathematical programs with equilibrium constraints

A kind of mathematical programs with equilibrium constraints （MPEC） is studied. By using the idea of successive approximation, a smoothing nonlinear programming, which is equivalent to the MPEC problem, is proposed. Thereby, it is ensured that some classical optimization methods can be applied for the MPEC problem. In the end, two algorithm models are proposed with the detail analysis of the global convergence.

Optimality Conditions for Double-sparsity Constrained Optimization

Sparse optimization has witnessed advancements in recent decades,and the step function finds extensive applications across various machine learning and signal processing domains.This paper integrates zero norm and the step function to formulate a doublesparsity constrained optimization problem,wherein a linear equality constraint is also taken into consideration.By defining aτ-Lagrangian stationary point and a KKT point,we establish the first-order and second-order necessary and sufficient optimality conditions for the problem.Furthermore,we thoroughly elucidate their relationships to local and global optimal solutions.Finally,special cases and examples are presented to illustrate the obtained theorems.

A Class of Smoothing-regularization Methods to Mathematical Programs with Vanishing Constraints

this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.

Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation

This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.

Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs

In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.

EXPONENTIAL CONVERGENCE OF SAMPLE AVERAGE APPROXIMATION METHODS FOR A CLASS OF STOCHASTIC MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

In this paper, we propose a Sample Average Approximation （SAA） method for a class of Stochastic Mathematical Programs with Complementarity Constraints （SMPCC） recently considered by Birbil, G/irkan and Listes [3]. We study the statistical properties of obtained SAA estimators. In particular we show that under moderate conditions a sequence of weak stationary points of SAA programs converge to a weak stationary point of the true problem with probability approaching one at exponential rate as the sample size tends to infinity. To implement the SAA method more efficiently, we incorporate the method with some techniques such as Scholtes＇ regularization method and the well known smoothing NCP method. Some preliminary numerical results are reported.

A Trust Region Algorithm for Solving Bilevel Programming Problems

In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.

Spectral fluctuations in the interacting boson model

The energy dependence of the spectral fluctuations in the interacting boson model(IBM)and its connections to the mean-field structures are analyzed by adopting two statistical measures:the nearest neighbor level spacing distribution P(S)measuring the chaoticity(regularity)in energy spectra and the Δ_(3)(L)statistics of Dyson and Metha measuring the spectral rigidity.Specifically,the statistical results as functions of the energy cutoff are determined for different dynamical scenarios,including the U(5)-SU(3)and SU(3)-O(6)transitions as well as those near the AW arc of regularity.We observe that most of the changes in spectral fluctuations are triggered near the stationary points of the classical potential,particularly for cases in the deformed region of the IBM phase diagram.Thus,the results justify the stationary point effects from the perspective of statistics.In addition,the approximate degeneracies in the 2^(+)spectrum on the AW arc is also revealed from the statistical calculations.

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

In this paper,a bilevel multiobjective programming problem,where the lower level is a convex parameter multiobjective program,is concerned.Using the KKT optimality conditions of the lower level problem,this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem.Then,a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced.It is shown that the Pareto optimal solutions(stationary points)of the approximate problems converge to a Pareto optimal solution(stationary point)of the original bilevel multiobjective programming problem.Numerical results showing the viability of the smoothing approach are reported.