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Stochastic variational inequalities (SVIs) have been used widely in modelling various optimization and equilibrium problems subject to data uncertainty. The sample average approximation (SAA) solution is an asymptotically consistent point estimator for the true solution to a stochastic variational inequality. Some central limit results and large deviation estimates for the SAA solution have been obtained. The purpose of this paper is to study the convergences in regimes of moderate deviations for the SAA solution. Using the delta method and the exponential approximation, we establish some results on moderate deviations. We apply the results to the hypotheses testing for the SVIs, and prove that the rejection region constructed by the central limit theorem has the probability of the type II error with exponential decay speed. We also give some simulations and numerical results for the tail probabilities. [ABSTRACT FROM AUTHOR]

This paper focuses on the cardinality constrained mean-variance portfolio optimization, in which only a small number of assets are invested. We first treat the covariance matrix of asset returns as a diagonal matrix with a special matrix processing technique. Using the dual theory, we formulate the lower bound problem of the original problem as a max-min optimization. For the inner minimization problem with the cardinality constraint, we obtain its analytical solution for the portfolio weights. Then, the lower bound problem turns out to be a simple concave optimization with respect to the Lagrangian multipliers. Thus, the interval split method and the supergradient method are developed to solve it. Based on the precise lower bound, the depth-first branch and bound method are designed to find the global optimal investment selection strategy. Compared with other lower bounds and the current popular mixed integer programming solvers, such as CPLEX and SCIP, the numerical experiments show that our method has a high searching efficiency. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12101317, 12271071, and 11991024], the Natural Science Foundation of Jiangsu Province [Grant BK20200819], the Team Project of Innovation Leading Talent in Chongqing [Grant CQYC20210309536], the Contract System Project of Chongqing Talent Plan [Grant cstc2022ycjh-bgzxm0147], and the Philosophy and Social Science Fund of Education Department of Jiangsu Province [Grant 2020SJA0168]. K.F.C. Yiu is supported in part by the Research Grants Council of Hong Hong [Grant PolyU 15223419], the Hong Kong Polytechnic University [Grants 4-ZZPT and 1-WZ0E], and the Research Centre for Quantitative Finance [Grant 1-CE03]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0344) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0344). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Optimal switching is a special class of optimal control problems for hybrid dynamic systems. In this paper, we consider the optimal switching problem of linear-quadratic switched systems. The aim is to design a suitable switching strategy with the constraint on the number of switchings so that the quadratical performance achieves the minimum value. This problem is difficult to be solved because of the tight coupling between the continuous switching time and the discrete switching sequence. In our method, we first divide this hybrid optimization problem into two subproblems. In each of them, only one type of variable is considered. Then, we develop a gradient-based method with the time-scaling transformation to process the optimal switching time problem and a branch and bound method based on a series of exact lower bounds to handle the optimal switching sequence problem, respectively. By solving these two subproblems alternatively, the optimal switching strategy satisfying the constraint on the number of switchings can be obtained. Numerical examples are given to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, an optimal PID tuning method is proposed for a class of two-link manipulators. In particular, the control specifications of the manipulators are considered. By modeling the control specifications into state constraints, the optimal PID tuning problem is converted to an optimal parameters selection problem with state constraints. An exact penalty function based method is then utilized to handle the state constraints. The superior of the proposed method over an existing method is verified by carrying out an numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we establish some existence results for the solution of the generalized symmetric set-valued quasi-equilibrium problem (GSSQEP). The new forms of GSSQEP via improvement set and scalar generalized symmetric set-valued quasi-equilibrium problem (GSSQEP Δ for short) are also introduced. By using Kakutani–Fan–Glicksberg fixed point method, maximal element principle and nonlinear scalarization technique, we develop two classes of sufficient conditions for the existence of solutions to GSSQEP. The drawback of some existing work for this problem is overcome. Moreover, some applications to the symmetric set-valued equilibrium problem (SSEP), symmetric vector quasi-equilibrium problem (SVQEP) and the set-valued equilibrium problem (SEP) are also given in this paper. Our results improve a few existing ones in Fakhar and Zafarani [Generalized symmetric vector quasiequilibrium problems. J Optim Theory Appl. 2008;136:397–409], Farajzadeh et al. [On the existence of solutions of symmetric vector equilibrium problems via nonlinear scalarization. Bull Iran Math Soc. 2019;45:35–58], Fu [Symmetric vector quasi-equilibrium problems. J Math Anal Appl. 2003;285:708–713], Han et al. [Existence of solutions for symmetric vector set-valued quasi-equilibrium problems with applications. Pacific J Optim. 2018;14:31–49]. [ABSTRACT FROM AUTHOR]

This paper studies a continuous-time securities market where an agent, having a random investment horizon and a targeted terminal mean return, seeks to minimize the variance of a portfolio's return. Two situations are discussed, namely a deterministic time-varying density process and a stochastic density process. In contrast to [18], the variance of an investment portfolio is no longer minimal when all assets are invested in a risk-free security. Furthermore, the random investment horizon has a material effect on the efficient frontier. This provides some insights into the classical mutual fund theorem. [ABSTRACT FROM AUTHOR]