In this paper, we introduce
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-preinvex interval-valued function and establish the Hermite–Hadamard inequality for preinvex interval-valued functions by using interval-valued ...Riemann–Liouville fractional integrals. We obtain Hermite–Hadamard-type inequalities for the product of two interval-valued functions. Further, some examples are given to confirm our theoretical results.
The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the ...technique of fixed point theorems. For the sake of converting the proposed problems into integral equations, we construct Green functions and study their properties for three different types of boundary value problems. Examples are presented to demonstrate the validity of theoretical findings.
In this paper, we examine a semi-infinite interval-valued optimization problem with vanishing constraints (SIVOPVC) that lacks differentiability and involves constraints that tend to vanish. We give ...definitions of generalized convex functions along with supportive examples. We investigate duality theorems for the SIVOPVC problem. We establish these theorems by creating duality models, which establish a relationship between SIVOPVC and its corresponding dual models, assuming generalized convexity conditions. Some examples are also given to illustrate the results.
Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly ...developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field.
Component commonality is a well-known approach in manufacturing, where the same components are used for multiple products. It has been implemented by many established companies such as Airbus, Kodak, ...Toyota, etc. We consider a standard two-product inventory model with a common component. The demands for the products are independent random variables. Instead of the usual approach to minimize the total shortage quantity, we propose to minimize the total shortage cost. The resulting problem is a non-convex nonlinear mathematical program. We illustrate the use of a primal-dual proximal method to solve this problem by obtaining numerically the optimal allocations of components. In particular, we show that a higher unit shortage cost induces a higher allocation.
The modified Totient function of Carmichael λ(.) is revisited, where important properties have been highlighted. Particularly, an iterative scheme is given for calculating the λ(.) function. A ...comparison between the Euler φ and the reduced totient λ(.) functions aiming to quantify the reduction between is given.
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.
In this paper, we study the problem of minimizing a general quadratic function subject to a quadratic inequality constraint with a fixed number of additional linear inequality constraints. Under a ...regularity condition, we first introduce two convex quadratic relaxations (CQRs), under two different conditions, that are minimizing a linear objective function over two convex quadratic constraints with additional linear inequality constraints. Then, we discuss cases where the CQRs return the optimal solution of the problem, revealing new conditions under which the underlying problem admits strong Lagrangian duality and enjoys exact semidefinite optimization relaxation. Finally, under the given sufficient conditions, we present necessary and sufficient conditions for global optimality of the problem and obtain a form of S-lemma for a system of two quadratic and a fixed number of linear inequalities.
We suggest and analyze an iterative scheme for finding the approximate element of the common set of solutions of a system of variational inequalities, a mixed equilibrium problem, and a hierarchical ...fixed point problem in a real Hilbert space. Strong convergence of the proposed method is proved under some conditions. The results presented in this paper extend and improve some well-known results in the literature.
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