模糊多目标半定规划的最优性条件

将模糊集理论应用到多目标半定规划中来,提出了有约束的模糊多目标半定规划模型,并首次给出了其最优有效解的定义.通过构造确定的隶属度函数,将以矩阵为决策变量的模糊多目标半定规划转化为一种目标函数的某些分量由约束函数决定的确定性多目标半定规划,并证明了前者最优有效解与后者有效解的一致性.在此基础之上,讨论了二者的最优性条件.     

Regression analysis of right-censored failure time data with missing censoring indicators

This paper discusses regression analysis of right-censored failure time data when censoring indicators are missing for some subjects. Several methods have been developed for the analysis under different situations and especially, Goetghebeur and Ryan considered the situation where both the failure time and the censoring time follow the proportional hazards models marginally and developed an estimating equation approach. One limitation of their approach is that the two baseline hazard functions were assumed to be proportional to each other. We consider the same problem and present an efficient estimation procedure for regression parameters that does not require the proportionality assumption. An EM algorithm is developed and the method is evaluated by a simulation study, which indicates that the proposed methodology performs well for practical situations. An illustrative example is provided.     

Solving Bilevel Linear Programs Using Multiple Objective Linear Programming

We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm uses the relationship between multiple objective linear programs and bilevel linear programs along with results for minimizing a linear objective over the efficient set for a multiple objective problem. Results in multiple objective programming needed are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound algorithm when the number of leader variables is small.     

二氧化钛纳米晶/石墨烯复合物的制备及其光催化性能 (cited: 1)

以氧化石墨和TiO₂溶胶为前驱物,结合絮凝与水热技术制备了TiO₂纳米晶/石墨烯复合物,表征了产物的结构、形貌、孔隙率、光谱吸收性质. 结果表明：TiO₂纳米晶的存在一定程度上阻止了石墨烯片层的重组,TiO₂纳米晶/石墨烯复合物较单纯TiO₂材料具有更强的吸光性能、对亚甲基蓝分子更强的吸附性能以及更高的电荷分离效率. 在紫外光和太阳光下,TiO₂纳米晶/石墨烯复合物对亚甲基蓝的光催化降解效率均高于P25和纯TiO₂.     

A new method for detection of alpha particles in 1 mm thick polycarbonate detectors using 50 Hz – HV ECE method

Recent studies in our laboratory have proved that electrochemical etching (ECE) of polycarbonate track detectors (PCTD) under 50 Hz – high voltage (HV) field conditions has potentials for time-integrated heavy charged particle detection and dosimetry applications. The rationale in the study is the ECE process of alpha particle tracks in 1 mm thick PCTDs by a 50 Hz – HV generator at optimized ECE conditions. Tracks of 3.2 MeV alpha particles from a collimated beam of an ²⁴¹Am source degraded in air and background tracks were registered. The effects of HV and ECE duration on alpha track registration efficiency and track diameters were studied for 3 sets of 50 Hz – 4, 5 and 6 kV field conditions in a PEW solution (potassium hydroxide, ethanol and water) at 26 °C. The optimized ECE conditions obtained at this stage of development for 1 mm thick PCTDs are 50 Hz – 4 kV in PEW solution at 26 °C for 10 h. Alpha track registration efficiency at 3.2 MeV is about 30% with 37 ± 6 μm mean track diameter. The mean background track density at the above stated optimized conditions is about 571 ± 16 tracks.cm⁻² with a mean diameter of 65 ± 5 μm. All tracks are observable by the unaided eyes. The mean background track diameter is near two times larger than that of alpha particle tracks at the optimum conditions applied; they are easily distinguished against each other. This high background track density while at this stage of development seems a drawback for low dose and low fluence particle applications, it has minimal effects on high fluence ion detection applications. The simple 50 Hz – HV generator used proved to be convenient for efficient alpha track amplifications. Studies are underway for improvement of the method in particular for reducing background track density.     

The Roberts characterization of proper and unit interval graphs

In this note, a constructive proof that the classes of proper interval graphs and unit interval graphs coincide is given, a result originally established by Fred S. Roberts. Additionally, the proof yields a linear-time and space algorithm to compute a unit interval representation, given a proper interval graph as input.     

Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models

This paper proposes a new method that extends the efficient global optimization to address stochastic black-box systems. The method is based on a kriging meta-model that provides a global prediction of the objective values and a measure of prediction uncertainty at every point. The criterion for the infill sample selection is an augmented expected improvement function with desirable properties for stochastic responses. The method is empirically compared with the revised simplex search, the simultaneous perturbation stochastic approximation, and the DIRECT methods using six test problems from the literature. An application case study on an inventory system is also documented. The results suggest that the proposed method has excellent consistency and efficiency in finding global optimal solutions, and is particularly useful for expensive systems.     

Generalized (<Emphasis Type="Italic">F</Emphasis>,<Emphasis Type="Italic">ρ</Emphasis>)-Convexity and Duality in Nonsmooth Problems of Multiobjective Optimization

A mixed-type dual for a nonsmooth multiobjective optimization problem with inequality and equality constraints is formulated. We obtain weak and strong duality theorems for a mixed-type dual without requiring the regularity assumptions and the nonnegativeness of the Lagrange multipliers associated to the equality constraints. We apply also a nonsmooth constraint qualification for multiobjective programming to establish strong duality results. In this case, our constraint qualification assures the existence of positive Lagrange multipliers associated with the vector-valued objective function. This work was supported by Center of Excellence for Mathematics, University of Isfahan, Isfahan, Iran.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.