Parallel LQP alternating direction method for solving variational inequality problems with separable structure

In this paper, we propose a logarithmic-quadratic proximal alternating direction method for structured variational inequalities. The predictor is obtained by solving series of related systems of nonlinear equations, and the new iterate is obtained by a convex combination of the previous point and the one generated by a projection-type method along a new descent direction. Global convergence of the new method is proved under certain assumptions. Preliminary numerical experiments are included to verify the theoretical assertions of the proposed method.Qatar University Start-Up Grant: QUSG-CAS-DMSP-13/14-8.Scopu

Editorial: Some recent trends in variational inequalities and optimization problems with applications

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Mean-standard deviation-conditional value-at-risk portfolio optimization

The use of variance as a risk measure is limited by its non-coherentnature. On the other hand, standard deviation has been demonstrated as acoherent and effective measure of market volatility. This paper suggests theuse of standard deviation in portfolio optimization problems with cardinalityconstraints and short selling, specifically in the mean-conditional value-at riskframework. It is shown that, subject to certain conditions, this approach leadsto lower standard deviation. Empirical results obtained from experiments onthe SP index data set from 2016-2021 using various numbers of stocks andconfidence levels indicate that the proposed model outperforms existing modelsin terms of Sharpe ratios

Convergence of a Proximal Point Algorithm for Solving Minimization Problems

We introduce and consider a proximal point algorithm for solving minimization problems using the technique of Güler. This proximal point algorithm is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic distance-like functions. It can be seen as an extragradient iterative scheme. We prove the convergence rate of this new proximal point method under mild assumptions. Furthermore, it is shown that this estimate rate is better than the available ones

On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints

In this paper, we study the minimization of an indefinite quadratic function over theintersection of balls and linear inequality constraints (QOBL). Using the hyperplanesinduced by the intersection of each pair of balls, we show that the optimal solution ofQOBL can be found by solving several extended trust-region subproblems (e-TRS).To solve e-TRS, we use the alternating direction method of multipliers approach anda branch and bound algorithm. Numerical experiments show the efficiency of theproposed approach compared to the CVX and the extended adaptive ellipsoid-basedalgorithmThe authors would like to thank the reviewer for useful comments and suggestions and Qatar University for supporting their project under Grant NCBP-QUCP-CAS-2020-1

Portfolio Selection Problem Using CVaR Risk Measures Equipped with DEA, PSO, and ICA Algorithms

Investors always pay attention to the two factors of return and risk in portfolio optimization. There are different metrics for the calculation of the risk factor, among which the most important one is the Conditional Value at Risk (CVaR). On the other hand, Data Envelopment Analysis (DEA) can be used to form the optimal portfolio and evaluate its efficiency. In these models, the optimal portfolio is created by stocks or companies with high efficiency. Since the search space is vast in actual markets and there are limitations such as the number of assets and their weight, the optimization problem becomes difficult. Evolutionary algorithms are a powerful tool to deal with these difficulties. The automotive industry in Iran involves international automotive manufacturers. Hence, it is essential to investigate the market related to this industry and invest in it. Therefore, in this study we examined this market based on the price index of the automotive group, then optimized a portfolio of automotive companies using two methods. In the first method, the CVaR measurement was modeled by means of DEA, then Particle Swarm Optimization (PSO) and the Imperial Competitive Algorithm (ICA) were used to solve the proposed model. In the second method, PSO and ICA were applied to solve the CVaR model, and the efficiency of the portfolios of the automotive companies was analyzed. Then, these methods were compared with the classic Mean-CVaR model. The results showed that the automotive price index was skewed to the right, and there was a possibility of an increase in return. Most companies showed favorable efficiency. This was displayed the return of the portfolio produced using the DEA-Mean-CVaR model increased because the investment proposal was basedon the stock with the highest expected return and was effective at three risk levels. It was found that when solving the Mean-CVaR model with evolutionary algorithms, the risk decreased. The efficient boundary of the PSO algorithm was higher than that of the ICA algorithm, and it displayed more efficient portfolios.Therefore, this algorithm was more successful in optimizing the portfolio