On solving three classes of nonlinear programming problems via simple differentiable penalty functions

We consider the following classes of nonlinear programming problems: the minimization of smooth functions subject to general constraints and simple bounds on the variables; the nonlinearl ₁-problem; and the minimax problem. Numerically reliable methods for solving problems in each of these classes, based upon exploiting the structure of the problem in constructing simple differentiable penalty functions, are presented.This research was made possible by NSERC Grant No. A8442.The author would like to thank Mrs. J. Selwood of the Department of Combinatories and Optimization, University of Waterloo, Ontario, Canada for her excellent typesetting.This work was carried out in the Department of Combinatories and Optimization, University of Waterloo, Waterloo, Ontario, Canada.     

LMI Approach to Robust Delay-Dependent Mixed H 2/H ∞ Controller of Uncertain Neutral Systems with Discrete and Distributed Time-Varying Delays

The design of a robust mixed H ₂/H _∞ controller for a class of uncertain neutral systems with discrete, distributed, and input time-varying delays is considered. More precisely, the proposed robust mixed H ₂/H _∞ controller minimizes an upper bound of the H ₂ performance measure, while guaranteeing an H _∞ norm bound constraint. Based on the Lyapunov-Krasovskii functional theory, a delay-dependent criterion is derived for the existence of a desired mixed H ₂/H _∞ controller, which can be constructed easily via feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem satisfying some LMI constraints is formulated to obtain a suboptimal robust mixed H ₂/H _∞ controller achieving the minimization of an upper bound of the closed-loop H ₂ performance measure. Finally, a numerical example is illustrated to show the usefulness of the obtained design method.The research reported here was supported by the National Science Council of Taiwan, ROC under Grant NSC 94-2213-E-507-002.     

T D property and spatial sublocales

As one of main backgrounds of locale theory, topologies have close connections with locales. But locales have other backgrounds such as algebra, mathematical logic, etc. So there are many differences between locales and topologies. Spatiality is an important localic property to investigate the connections between locales and topologies. TheT _D property is a special separation property which plays an important role in this kind of investigations. Just as it will be proved in this paper, theT _D property often appears as the lowest requirement for many topological spaces such that they can be described with localic properties and vice versa. In this paper, we show these special properties of theT _D axiom and investigate some other interesting and important problems ofT _D -spatiality of locales.Supported by the National Natural Science Foundation of China and the Science Foundation of the State Education Commision of China.Supported by the Fund for Excellent Young University Teachers of the State Educational Commission of China and theE _x -Oversea-Scholars Fund of the Educational Commission of China.     

A. S. Convergence of two-parameter banach space valued martingales and the radon-nikodym property of banach spaces

In this paper, we prove that under theF ₄ conditions, anyL log⁺ L bounded two-parameter Banach spece valued martingale converges almost surely to an integrable Banach space valued random variable if and only if the Banach space has the Radon-Nikodym property. We further prove that the above conclusion remains true if theF ₄ condition is replaced by the weaker localF ₄ condition. Project supported by the National Natural Science Foundation of China and the State Education Commission Ph. D. Station Foundation     

Linear best approximation using a class ofk-majorl p norms

Consideration is given to problems of linear best approximation using a variant of the usuall _p norms referred to ask-majorl _p norms, for the cases when 1<p<. The underlying problem is the minimization of a piecewise smooth function. Best approximations are characterized, and a descent algorithm is developed.     

Structural results for partially observed control models

A general partially observed control model with discrete time parameter is investigated. Our main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, we show how the value functions depend on the observation kernels and we present conditions for a lower bound of an optimal policy. Our approach is based on two multivariate stochastic orderings: theTP ₂ ordering and the Blackwell ordering.Dedicated to Prof. Dr. K. Hinderer on the occassion of his 60^th birthday     

The infinite server queue and heuristic approximations to the multi-server queue with and without retrials

In this paper, properties of the time-dependent state probabilities of theM _t /G/∞ queue, when the queue is assumed to start empty are studied. Those results are compared with corresponding time-dependent results for theM/M/1 queue. Approximation to the time-dependent state probabilities of theM/G/m/m queue by means of the corresponding time-dependent state probabilities of theM/G/∞ queue are discussed. Through a decomposition formula it is shown that the main performance characteristics of the ergodicM/M/m/m+d queue are sums of the corresponding random variables for the ergodicM/M/m/m andM/M/1/1+(d−1) queues, respectively, weighted by the 3-rd Erlang formula (stationary probability of waiting or being lost for theM/M/m/m+d queue). Successful exact and approximation extensions of this kind of decomposition formula to theM/M/m/m+d queue with retrials are presented.     

Controller design to optimize a composite performance measure

This paper studies a mixed objective problem of minimizing a composite measure of thel ₁, ₂, andl -norms together with thel -norm of the step response of the closed loop. This performance index can be used to generate Pareto-optimal solutions with respect to the individual measures. The problem is analyzed for discrete-time, single-input single-output (SISO), linear time-invariant systems. It is shown via Lagrange duality theory that the problem can be reduced to a convex optimization problem with a priori known dimension. In addition, continuity of the unique optimal solution with respect to changes in the coefficients of the linear combination that defines the performance measure is estabilished.This research was supported by the National Science Foundation under Grants No. ECS-92-04309, ECS-92-16690 and ECS-93-08481.     

Linear programming via a quadratic penalty function

We use quadratic penalty functions along with some recent ideas from linearl ₁ estimation to arrive at a new characterization of primal optimal solutions in linear programs. The algorithmic implications of this analysis are studied, and a new, finite penalty algorithm for linear programming is designed. Preliminary computational results are presented.Research supported by grant No. 11-0505 from the Danish Natural Science Research Council SNF.     

Effect of A-site cation substitution on magnetic transition temperature of (LaCa) MnO3

The ferromagnetic transition temperatures have been measured on two bathes of perovskite manganese oxides such as (La_1-x R _x )_2/3Ca_1/3MnO₃(R=Ce, Pr, Nd, etc.) and La_2/3(Ca_1-y Cd _y )_1/3MnO₃. It is found that the (La_1-x R _x )_2/3Ca_1/3MnO₃ samples have obviously different Curie temperatureT _C although their (r_A) (the average A-site cation radius) are almost identical, and theT _C in the system of (La_1-x R _x )_2/3Ca_1/3MnO₃(R=Ce, Pr, Nd, etc.) and La_2/3(Ca_1-y Cd _y )_1/3MnO₃. It is found that the (La_1-x R _x )_2/3Ca_1/3MnO₃ compounds increases with increasingy although (r_A) decreases slightly. It is suggested that the Curie temperature should be influenced by the average local A-site magnetic moment in the ferromagnetic perovskite manganite system. Project supported by the National Natural Science Foundation of China (Grant No. 19504012) and the Chinese Academy of Sciences.