Narrow Results

In this paper, we intend to make a new approach to introduce the concept of t_n-statistical convergence of complex uncertain sequences like t_n-statistical convergence almost surely (a.s.), t_n-statistical convergence in measure, t_n-statistical convergence in mean, t_n-statistical convergence in distribution and t_n-statistical convergence in uniformly almost surely (u.a.s). Various inclusion relations are established between newly formed sequence spaces.

Investors usually invest not only in risky assets but also in risk-free assets and face not only portfolio risk but also background risk. This paper discusses an uncertain portfolio selection problem in risky assets and risk-free assets with monotone increasing multiplicative background risk (MBR), which is prevalent but less research has been done. To do so, we first propose an uncertain mean-risk index model based on uncertainty theory where the security return and MBR are regarded as uncertain variables and give the deterministic form of the model. Then for further analysis, we discuss the critical constraint and optimality condition of the model. Based on the discussion, we study the influence of uncertain MBR on the investors’ decisions. Finally, we provide the case analysis to illustrate the application of our method and the analysis results.

This study is focused on robust design optimization (RDO) of the tuned mass dampers (TMDs), which are widely used as a passive vibration controller in structural systems. The performance of the TMDs designed under the implicit assumption that all relevant system parameters (such as loading and structural characteristics) are deterministic is greatly affected by the inevitable inherent uncertainties in the system parameters. In this regard, a framework is proposed for the RDO of TMDs to determine its optimal solution which is less sensitive to system parameter variability. RDO is defined as a multi-objective optimization problem that aims to minimize the mean and variance of the performance function. In the case of multiple TMDs, the proposed framework uniquely avoids the presumption of their mass distribution, number, and placement location. In the proposed RDO framework, an augmented formulation is adopted wherein the design parameters are artificially introduced as uncertain variables with some prescribed probability density function (PDF) over the design space. The resulting optimization problem is solved using the stochastic subset optimization (SSO) and KN, a direct search optimization method. The effectiveness of the proposed framework is studied by analyzing four illustrative examples involving a single TMD attached to a single-degree-of-freedom (SDOF) structure, a single TMD attached to a multiple-degree-of-freedom (MDOF) structure, multiple TMDs attached to an MDOF structure, and an 80-story structure equipped with multiple TMDs.

This paper focuses on the computation issue of portfolio optimization with scenario-based mean-average value at Risk (AVaR) in uncertain environment. The portfolio optimization problem is designed in two cases: risk-taker and risk-averse models. The main idea is to replace the portfolio selection models with linear programming (LP) problems. Since the computing time required for solving LP greatly depends on the dimension and the structure of the problem, the conventional numerical methods are usually less effective in real-time applications. One promising approach to handle online applications is to employ recurrent neural networks based on circuit implementation. Hence, according to the convex optimization theory and some concepts of ordinary differential equations, a neural network model for solving the LP problems related to portfolio selection problems is presented. The equilibrium point of the proposed model is proved to be equivalent to the optimal solution of the original problem. It is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns. Some illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.