MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.

Optimization Mathematical Model of Pile Forces for Offshore Piled Breasting Dolphins

An optimization mathematical model of the pile forces for piled breasting dolphins in the open sea under various loading conditions is presented. The optimum layout with the well distributed pile forces and the least number of piles is achieved by the multiplier penalty function method. Several engineering cases have been calculated and compared with the result of the conventional design method. It is shown that the number of piles can be reduced at least by 10%～20% and the piles' bearing state is improved greatly.

An Exact Logarithmic-exponential Multiplier Penalty Function

In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the global optimizers of a nonlinear problem are precisely the global optimizers of the logarithmic-exponential multiplier penalty problem.

Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems

The paper deals with the g2-stability analysis of multi-input-multi-output （MIMO） systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin- earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general g2-stability conditions in the frequency domain. These conditions have the following features： i） They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block, ii） For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.

Analysis on a Superlinearly Convergent Augmented Lagrangian Method

The augmented Lagrangian method is a classical method for solving constrained optimization.Recently,the augmented Lagrangian method attracts much attention due to its applications to sparse optimization in compressive sensing and low rank matrix optimization problems.However,most Lagrangian methods use first order information to update the Lagrange multipliers,which lead to only linear convergence.In this paper,we study an update technique based on second order information and prove that superlinear convergence can be obtained.Theoretical properties of the update formula are given and some implementation issues regarding the new update are also discussed.

Frequency-domain stability criteria for SISO and MIMO nonlinear feedback systems with constant and variable time-delays

New frequency-domain criteria are proposed for the L2-stability of both nonlinear single-input-single-output （SISO） and nonlinear multiple-input-multiple-output （MIMO） feedback systems, described by nonlinear integral equations. For SISO systems, the feedback block is a constant scalar gain in product with a linear combination of first-and-third-quadrant scalar nonlinearities （FATQNs） with time-delay argument functions; and, for MIMO systems, it is a constant matrix gain in product with a linear combination of vector FATQNs also with time-delay argument functions. In both the cases, the delay function in the arguments of the nonlinearities may be, in general, i） zero, ii） a constant, iii） variable-time and iv） fixed-history （only for SISO systems）. The stability criteria are derived from certain recently introduced algebraic inequalities concerning the scalar and vector nonlinearities, and involve the causal＋anticausal O＇Shea-Zames-Falb multiplier function （scalar for SISO systems and matrix for MIMO systems）. Its time-domain gl-norm is constrained by the coefficients and characteristic parameters （CPs） of the nonlinearities and, in the case of the time-varying delay, by its rate of variation also. The stability criteria, which are independent of Lyapunov-Krasovskii or Lyapunov-Razumikhin functions and do not seem to be derivable by invoking linear matrix inequalities, seem to be the first of their kind. Two numerical examples for each of SISO and MIMO systems illustrate the criteria.

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.