Papers by Vasilios Katsikis
Computers & Operations Research
IEEE Transactions on Fuzzy Systems
Neural Computing and Applications
This paper provides the construction of a powerful and efficient computational method, that trans... more This paper provides the construction of a powerful and efficient computational method, that translates Polyrakis algorithm [I.A. Polyrakis, Minimal lattice-subspaces, Trans. Am. Math. Soc. 351 (1999) 4183-4203, Theorem 3.19] for the calculation of lattice-subspaces and vector sublattices in R n. In the theory of finance, lattice-subspaces have been extensively used in order to provide a characterization of market structures in which the costminimizing portfolio is price-independent. Specifically, we apply our computational method in order to solve a cost minimization problem that ensures the minimum-cost insured portfolio.
This paper provides the construction of a powerful and efficient computational method, that trans... more This paper provides the construction of a powerful and efficient computational method, that translates Polyrakis algorithm [I.A. Polyrakis, Minimal lattice-subspaces, Trans. Am. Math. Soc. 351 (1999) 4183-4203, Theorem 3.19] for the calculation of lattice-subspaces and vector sublattices in R n. In the theory of finance, lattice-subspaces have been extensively used in order to provide a characterization of market structures in which the costminimizing portfolio is price-independent. Specifically, we apply our computational method in order to solve a cost minimization problem that ensures the minimum-cost insured portfolio.
Applied Mathematics and Computation
Axioms
Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require ta... more Some decision-making problems, i.e., multi-criteria decision analysis (MCDA) problems, require taking into account the attitudes of a large number of decision-makers and/or respondents. Therefore, an approach to the transformation of crisp ratings, collected from respondents, in grey interval numbers form based on the median of collected scores, i.e., ratings, is considered in this article. In this way, the simplicity of collecting respondents’ attitudes using crisp values, i.e., by applying some form of Likert scale, is combined with the advantages that can be achieved by using grey interval numbers. In this way, a grey extension of MCDA methods is obtained. The application of the proposed approach was considered in the example of evaluating the websites of tourism organizations by using several MCDA methods. Additionally, an analysis of the application of the proposed approach in the case of a large number of respondents, done in Python, is presented. The advantages of the propose...
Science China Information Sciences
Neural Processing Letters
Journal of Modeling and Optimization
The minimization of the costs related to portfolio insurance is a very important investment strat... more The minimization of the costs related to portfolio insurance is a very important investment strategy. In this article, by adding the transaction costs to the classical minimum cost portfolio insurance (MCPI) problem, we define and study the MCPI under transaction costs (MCPITC) problem as a nonlinear programming (NLP) problem. In this way, the MCPI problem becomes more realistic. Since such NLP problems are commonly solved by heuristics, we use the Beetle Antennae Search (BAS) algorithm to provide a solution to the MCPITC problem. Numerical experiments and computer simulations in real-world data sets confirm that our approach is an excellent alternative to other evolutionary computation algorithms.
Mathematical Methods in the Applied Sciences
IEEE/CAA Journal of Automatica Sinica
In this paper, we propose enhancements to Beetle Antennae search (BAS) algorithm, called BAS-ADAM... more In this paper, we propose enhancements to Beetle Antennae search (BAS) algorithm, called BAS-ADAM, to smoothen the convergence behavior and avoid trapping in local-minima for a highly non-convex objective function. We achieve this by adaptively adjusting the step-size in each iteration using the adaptive moment estimation (ADAM) update rule. The proposed algorithm also increases the convergence rate in a narrow valley. A key feature of the ADAM update rule is the ability to adjust the step-size for each dimension separately instead of using the same step-size. Since ADAM is traditionally used with gradient-based optimization algorithms, therefore we first propose a gradient estimation model without the need to differentiate the objective function. Resultantly, it demonstrates excellent performance and fast convergence rate in searching for the optimum of non-convex functions. The efficiency of the proposed algorithm was tested on three different benchmark problems, including the training of a high-dimensional neural network. The performance is compared with particle swarm optimizer (PSO) and the original BAS algorithm.
IEEE Access
The problem of portfolio management relates to the selection of optimal stocks, which results in ... more The problem of portfolio management relates to the selection of optimal stocks, which results in a maximum return to the investor while minimizing the loss. Traditional approaches usually model the portfolio selection as a convex optimization problem and require the calculation of gradient. Note that gradient-based methods can stuck at local optimum for complex problems and the simplification of portfolio optimization to convex, and further solved using gradient-based methods, is at a high cost of solution accuracy. In this paper, we formulate a nonconvex model for the portfolio selection problem, which considers the transaction cost and cardinality constraint, thus better reflecting the decisive factor affecting the selection of portfolio in the real-world. Additionally, constraints are put into the objective function as penalty terms to enforce the restriction. Note that this reformulated problem cannot be readily solved by traditional methods based on gradient search due to its nonconvexity. Then, we apply the Beetle Antennae Search (BAS), a nature-inspired metaheuristic optimization algorithm capable of efficient global optimization, to solve the problem. We used a large real-world dataset containing historical stock prices to demonstrate the efficiency of the proposed algorithm in practical scenarios. Extensive experimental results are presented to further demonstrate the efficacy and scalability of the BAS algorithm. The comparative results are also performed using Particle Swarm Optimizer (PSO), Genetic Algorithm (GA), Pattern Search (PS), and gradient-based fmincon (interior-point search) as benchmarks. The comparison results show that the BAS algorithm is six times faster in the worst case (25 times in the best case) as compared to the rival algorithms while achieving the same level of performance. INDEX TERMS Portfolio management, constrained optimization, nature-inspired algorithms, beetle search optimization.
Computational and Applied Mathematics
Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some cha... more Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific algebraic approach, based on proposed definitions and previously verified properties. The approach used here is new even in the matrix case.
Neural Processing Letters
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Neural Processing Letters
Applied Mathematics and Computation
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Papers by Vasilios Katsikis