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:
By using the penalty function method with objective parameters, the paper presents an interactive algorithm to solve the inequality constrained multi-objective programming (MP). The MP is transformed into a single objective optimal problem (SOOP) with inequality constrains; and it is proved that, under some conditions, an optimal solution to SOOP is a Pareto efficient solution to MP. Then, an interactive algorithm of MP is designed accordingly. Numerical examples show that the algorithm can find a satisfactory solution to MP with objective weight value adjusted by decision maker.

Abstract:
In this paper, we present an algorithm to solve the inequality constrained multi-objective programming (MP) by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem (UPOP) is defined. Under some conditions, a Pareto efficient solution (or a weakly-efficient solution) to UPOP is proved to be a Pareto efficient solution (or a weakly-efficient solution) to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.

Abstract:
The paper develops a multi-product supply chain model where supplyproduction-
sale integration is considered and the worst-case conditional value
at risk (WCVaR) model is applied as the risk measure, and also provides a
coordination strategy to minimize the supply chain risk. First, by analyzing
the source demand of market in the supply chain, three WCVaR models consisting
of three tiers—the supplier, the manufacturer and the retailer in the
supply chain are proposed to measure the market risk. Then, a risk coordination
model is proposed to cover the whole supply chain including producing,
order, inventory and sales. Finally, the numerical results show the efficiency of
the model in mitigating risks. And we make a summary of supply chain risk
management strategies.

Abstract:
This paper extends an existing cooperative multi-objective interaction programming problem with interaction constraint for two players (or two agents). First, we define an s-optimal joint solution with weight vector to multi-objective interaction programming problem with interaction constraint for two players and get some properties of it. It is proved that the s-optimal joint solution with weight vector to the multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Then, we define another s-optimal joint solution with weight value to multi-objective interaction programming problem with interaction constraint for two players and get some of its properties. It is proved that the s-optimal joint solution with weight vector to multi-objective interaction programming problem can be obtained by solving a corresponding mathematical programming problem. Finally, we build a pricing multi-objective interaction programming model for a bi-level supply chain. Numerical results show that the interaction programming pricing model is better than Stackelberg pricing model and the joint pricing model.

Abstract:
EcR (ecdysone receptor)-mediated ecdysone signaling pathway contributes to regulate the transcription of genes involved in various processes during insect development. In this work, we detected the expression of EcR gene in silkworm ovary-derived BmN4 cells and found that EcR RNAi result in an alteration of cell shape, indicating that EcR may orchestrate cell cycle progression. EcR RNAi and EcR overexpression analysis revealed that in the cultured BmN4 cells, EcR respectively promoted and suppressed the transcription of E2F-1 and CycE, two genes controlling cell cycle progression. Further examination demonstrated that ecdysone application in BmN4 cells not only changed the transcription of these two cell cycle genes like that under EcR overexpression, but also induced cell cycle arrest at G2/M phase. In vivo analysis confirmed that E2F-1 expression was elevated in silk gland of silkworm larvae after ecdysone application, which is same as its response to ecdysone in BmN4 cells. However, ecdysone also promotes CycE transcription in silk gland, and this is converse with the observation in BmN4 cells. These results provide new insights into understanding the roles of EcR-mediated ecdysone signaling in the regulation of cell cycle.

Abstract:
In this paper,under given some condition we have proved existence of the subdifferential of the point sets mapping in local convex topological vector spaces. Meanwhile, we have gotten stability for the subdifferential of cone efficient point(solution) sets and cone weakly efficient point(solution) sets of multiobjective programming with respect to perturbation of cone respectively.

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.