修正PRP共轭梯度方法求解无约束最优化问题

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

Sensitivity analysis of the greatest eigenvalue of a symmetric matrix via the ɛ-subdifferential of the associated convex quadratic form

LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR ^m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.     

Constrained minimax approximation and optimal preconditioned for Toeplitz matrices

A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented.     

Design, Synthesis and Investigation of Bone Affinity of the Conjugates of 5-Fluorouracil and Hydroxybisphosphonate

Bone tumor, as a common disease, is treated by surgical resection, radiotherapy and chemotherapy. Chemotherapy is one of the most important treatment, however, a major problem of chemotherapy is lack of selectivity of cytotoxic drugs. Although many attempts have been made to increase the selectivity of therapeutic drugs for the bone diseases, such as osteoporosis, paget’s, hypercalcemia and bone metastases by conjugating them with targeting carriers1-4, there are still no bone-targeting agent…     

High-performance liquid chromatography with continuous gradient elution in screening for unknown metabolites of butoprozine directly in dog bile

This paper describes the screening for metabolites of butoprozine, a new anti-anginal drug, in dog bile by means of reverse-phase HPLC. Although it does involve a simple clean-up step to remove a substantial amount of endogenous bile compounds, this screening method nevertheless avoids extraction of metabolites and thus allows all metabolites to be introduced into the chromatographic system. A single run of 100 minutes from 100% water to 100% methanol in a linear gradient effects adequate separation of the great majority of metabolites without interference from remaining endogenous compounds. Two methods of differentiating between metabolite peaks and endogenous peaks have been worked out. The first one makes use of ¹⁴C-labeled butoprozine by measuring the amount of radioactivity in the column effluent while simultaneously recording the UV absorbance. The second method compares continuous gradient chromatograms of bile recorded before and after butoprozine administration under very similar conditions. The latter method can be applied to both radioactive and non-radioactive materials.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

2-Cyanoacrylates in the conjugate addition of trifluoroacetic acid and nucleophilic reagents

In the presence of trifluoroacetic acid, ethyl 2-cyanoacrylate readily reacts with nucleophilic reagents, such as 2-chloro-1,3,2-benzodioxaphosphole, (EtO)₃P, (EtO)₂PCl, Ph₂PCl, Ph₃P, and thiourea. In these reactions the acid proton enters position 2 of the cyanoacrylate, whereas the nucleophilic component enters position 3, in accordance with the electron density distribution in the acrylate. In the absence of trifluoroacetic acid the above reagents, except 2-chloro-1,3,2-benzodioxaphosphole, cause ethyl 2-cyanoacrylate polymerization. The interaction of ethyl 2-cyanoacrylate with 2-chloro-1,3,2-benzodioxaphosphole and trifluoroacetic acid is the first example of a 2-cyanoacrylate taking part in the acid-initiated electrophilic conjugate addition of a weak nucleophile.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1245–1247, July, 1993.     

Nondifferential optimization via adaptive smoothing

The problem of minimizing a nondifferential functionx f(x) (subject, possibly, to nondifferential constraints) is considered. Conventional algorithms are employed for minimizing a differential approximationf off (subject to differentiable approximations ofg). The parameter is adaptively reduced in such a way as to ensure convergence to points satisfying necessary conditions of optimality for the original problem.This research was supported by the UK Science and Engineering Research Council, the National Science Foundation under Grant No. ECS-8121149, and the Joint Services Electronics Program, Contract No. F49620-79-C-0178.     

Optimization of upper semidifferentiable functions

In this paper, we present an implementable algorithm to minimize a nonconvex, nondifferentiable function in ^m . The method generalizes Wolfe's algorithm for convex functions and Mifflin's algorithm for semismooth functions to a broader class of functions, so-called upper semidifferentiable. With this objective, we define a new enlargement of Clarke's generalized gradient that recovers, in special cases, the enlargement proposed by Goldstein. We analyze the convergence of the method and discuss some numerical experiments.The author would like to thank J. B. Hiriart-Urruty (Toulouse) for having provided him with Definition 2.1 and the referees for their constructive remarks about a first version of the paper.