Dual conditions characterizing optimality for convex multi-objective programs

Received June 13, 1995 / Revised version received February 6, 1998 Published online August 18, 1998     

Evolutionary model of the growth and size of firms

The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat’s law of proportionate effects as the result of the competition between products. Applying a preferential attachment mechanism for firms, the theory allows to establish the size distribution of products and firms. Also established are the growth rate and price distribution of consumer goods. Taking into account the characteristic property of human activities to occur in bursts, the model allows also an explanation of the size–variance relationship of the growth rate distribution of products and firms. Further the product life cycle, the learning (experience) curve and the market size in terms of the mean number of firms that can survive in a market are derived. The model also suggests the existence of an invariant of a market as the ratio of total profit to total revenue. The relationship between a neo-classic and an evolutionary view of a market is discussed. The comparison with empirical investigations suggests that the theory is able to describe the main stylized facts concerning the size and growth of firms.     

Infinite horizon multiobjective optimal control problems in the discrete time case

This article studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case. The functions appearing in the problems satisfy smoothness conditions. This article generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations or difference inequations. Necessary conditions of Pareto optimality are presented, namely Pontryagin maximum principles in the weak form and in the strong form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge.     

Some kind of Pareto stationarity for multiobjective problems with equilibrium constraints

ABSTRACT

In this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC.     

Characterization through distributional properties of dual generalized order statistics

Distributional properties of two non-adjacent dual generalized order statistics have been used to characterize distributions. Further, one sided contraction and dilation for the dual generalized order statistics are discussed and then the results are deduced for generalized order statistics, order statistics, lower record statistics, upper record statistics and adjacent dual generalized order statistics.     

CONSTRAINED MULTIOBJECTIVE GAMES IN LOCALLY CONVEX H-SPACES

IntroductionTheconceptofanequilibriumpointforann_persongamewasfirstintroducedbyNash[1,2 ],whoestablishedtheexistenceoftheequilibriumpointundercertainassumptions.Sincethen ,theNashequilibriumproblemforn_persongameshavebeenintensivelystudiedandextendedbyanumberofauthorsundervariousassumptionsanddifferentdirections.Theconstrainedgameswithfiniteorinfiniteplayersisanimportantgeneralizationofn_persongameswhichhavebeenwidelystudiedbymanyauthors.Recently ,muchattentionhasbeenfocusedonthegameproblemsw…     

改进的多目标粒子群算法

提出了一个改进的粒子群算法并将其用于解决多目标优化问题．该算法利用粒子群算法的信息传递机制，引入多目标演化算法常用的归档技术，采用SPEA2算法的环境选择和配对选择策略，使得整个群体在保持适当的选择压力的情况下收敛于Pareto最优解集．标准测试函数的数值实验结果表明，所提出的算法能够使找到的解集快速收敛到Pareto非劣最优目标域，并且解集沿着Pareto非劣最优目标域有很好的扩展性．     

MULTI-OBJECTIVE OPTIMIZATION AND AERODYNAMIC PERFORMANCE ANALYSIS OF THE UPPER SURFACE FOR HYPERSONIC VEHICLES

为分析小攻角巡航条件下吸气式高超声速飞行器上壁面的变化对其气动性能和容积的影响, 以参数化后的飞行器上壁面对称面型线为设计变量, 在飞行马赫数6.5, 飞行高度27 km, 飞行攻角为4°的条件下, 采用计算流体力学为性能分析工具, Pareto多目标遗传算法为优化设计方法, 开展了二维条件下的升阻比/容积双目标优化设计. 在此基础上, 选择典型的二维优化结果, 重构生成对应的三维构型并进行数值分析, 获得了飞行器气动性能和容积间的相互关系. 结果表明在巡航条件下, 尽管二维/三维条件下飞行器的气动参数数值有较大差别, 但在这2种条件下, 飞行器的升阻比和容积间的关系均近似呈线性反比例关系. 同时, 对于三维构型而言, 在给定容积不变的条件下, 通过改变上壁面对称面型线的形状仅能使升阻比获得较小的增量(约0.36%). 相比之下, 当给定升阻比基本不变的条件下, 飞行器容积可调空间相对较大, 约为1.93%. 此外, 计算结果还表明, 在飞行器的容积基本不变情况下, 通过调节上壁面对称面型线, 可使飞行器的俯仰力矩获得5%左右的调节空间, 且其升阻比基本不变.     

Intensity‐based estimation of extreme loss event probability and value at risk

We develop a methodology for the estimation of extreme loss event probability and the value at risk, which takes into account both the magnitudes and the intensity of the extreme losses. Specifically, the extreme loss magnitudes are modeled with a generalized Pareto distribution, whereas their intensity is captured by an autoregressive conditional duration model, a type of self‐exciting point process. This allows for an explicit interaction between the magnitude of the past losses and the intensity of future extreme losses. The intensity is further used in the estimation of extreme loss event probability. The method is illustrated and backtested on 10 assets and compared with the established and baseline methods. The results show that our method outperforms the baseline methods, competes with an established method, and provides additional insight and interpretation into the prediction of extreme loss event probability. Copyright © 2012 John Wiley & Sons, Ltd.