Abstract:
In this paper, a new augmented Lagrangian penalty function for constrained optimization problems is studied. The dual properties of the augmented Lagrangian objective penalty function for constrained optimization problems are proved. Under some conditions, the saddle point of the augmented Lagrangian objective penalty function satisfies the first-order Karush-Kuhn-Tucker (KKT) condition. Especially, when the KKT condition holds for convex programming its saddle point exists. Based on the augmented Lagrangian objective penalty function, an algorithm is developed for finding a global solution to an inequality constrained optimization problem and its global convergence is also proved under some conditions.

Abstract:
In the paper we generalize the while-rule in Hoare calculus to an infinite one and then present a sufficient condition much weaker than the expressiveness for Cook‘2 relative completeness theorem with respect to our new axiomatic system.Using the extended Hoare calculus we can derive true Hoare formulas which contain while statements free of loop invariants.It is also pointed out that the weak condition is a first order property and therefore provides a possible approach to the characterization of relative completeness which is also a first order property.

Abstract:
The leading-order hadronic contribution to the muon magnetic anomaly a_{\mu} = (g_{\mu} - 2)/2, calculated using a dispersion integral of e+e- annihilation data and tau decay data, is briefly reviewed. This contribution has the largest uncertainty to the predicted value of a_{\mu}, which differs from the experimental value by ~3.6 (2.4) standard deviations for the e+e- (tau) based analysis. New results since the last workshop and main open issues on the subject are discussed.

Abstract:
We investigate the existence of periodic solutions of linear Hamiltonian systems with a nonlinear perturbation. Under generalized Ahmad-Lazer-Paul type coercive conditions for the nonlinearity on the kernel of the linear part, existence of periodic solutions is obtained by saddle point theorems. A note on a result of Rabinowitz is also given.

Abstract:
Results on multi-lepton events at high transverse momenta, isolated lepton events with large missing transverse energy and single W production reported to this conference are based for the first time on the full data samples taken by two colliding experiments, H1 and ZEUS, at HERA. The data correspond to an integrated luminosity of about 1fb-1 from both experiments.

Abstract:
Inclusive e^\pm p single and double differential cross sections for neutral (NC) and charged current (CC) deep inelastic scattering processes are measured with the H1 detector at HERA. The data were taken at a centre-of-mass energy of \sqrt{s} = 319 GeV with a total integrated luminosity of 327.8 pb^{-1} shared between two lepton beam charges and two longitudinal lepton polarisation modes. The differential cross sections are measured in the range of negative four-momentum transfer squared, Q2, between 60 and 50 000 GeV2, and Bjorken x between 0.0008 and 0.65. The measurements are combined with earlier published unpolarised H1 data to improve statistical precision and used to determine the structure function xF_3^{\gamma Z}. A measurement of the structure function F_2^{\gamma Z}, sensitive to parity violating effects in NC, is presented for the first time. The polarisation dependence of the CC total cross section is also measured. The new measurements are well described by a next-to-leading order QCD fit based on all published H1 inclusive cross section data which are used to extract the parton distribution functions of the proton.

Abstract:
A new Compton longitudinal polarimeter currently under construction for HERA is presented. The key component of the polarimeter is a Fabry-Perot cavity located around the electron beam pipe. With such an optical cavity, a continuous laser power equivalent to 5 kW, much higher than those commercially available, can be achieved, leading to one backscattered photon per bunch crossing. This ``few-photon mode'' will allow a very precise determination of the calorimeter response with little systematic uncertainty. The electron polarization measurement at the per mill level is expected.

Abstract:
New structure function results from H1 are presented. The measurements cover a huge kinematical range for Q^2, the four momentum transfer squared, from 0.35, GeV^2 to 30,000, GeV^2, and for Bjorken x between \sim 5\cdot 10^{-6} and 0.65. At Q^2>100, GeV^2, full HERA, I data have been analyzed. The data are compared with a new QCD analysis. The impact of the HERA, I data on the parton density functions is discussed.

Abstract:
The leading-order hadronic contribution to the muon magnetic anomaly a_{\mu} = (g_{\mu} - 2)/2, calculated using a dispersion integral of e+e- annihilation data and tau decay data, is briefly reviewed. This contribution has the largest uncertainty to the predicted value of a_{\mu}, which differs from the experimental value by ~3.6 (2.4) standard deviations for the e+e- (tau) based analysis. New results since the last workshop and main open issues on the subject are discussed.

Abstract:
The evolution of the determination of the strong coupling constant $\alpha_s$ from the leptonic branching ratios, the lifetime, and the invariant mass distributions of the hadronic final state of the $\tau$ lepton over the last two decades is briefly reviewed. The improvements in the latest ALEPH update are described in some detail. Currently this is one of the most precise $\alpha_s$ determinations. Together with the other determination at the $Z$ boson mass pole, they constitutes the most accurate test of the asymptotic freedom in QCD.