Search

The complexity of historical data in financial markets and the uncertainty of the future, as well as the idea that investors always expect the least risk and the greatest return. This study presents a multi-period fractional portfolio model in a fuzzy environment, taking into account the limitations of asset quantity, asset position, transaction cost, and inter-period investment. This is a mixed integer programming NP-hard problem. To overcome the problem, an improved genetic algorithm (IGA) is presented. The IGA contribution mostly involves the following three points: (i) A cardinal constraint processing approach is presented for the cardinal constraint conditions in the model; (ii) Logistic chaotic mapping was implemented to boost the initial population diversity; (iii) An adaptive golden section variation probability formula is developed to strike the right balance between exploration and development. To test the model's logic and the performance of the proposed algorithm, this study picks stock data from the Shanghai Stock Exchange 50 for simulated investing and examines portfolio strategies under various limitations. In addition, the numerical results of simulated investment are compared and analyzed, and the results show that the established models are in line with the actual market situation and the designed algorithm is effective, and the probability of obtaining the optimal value is more than 37.5% higher than other optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper constructs an interval partition linearization algorithm for solving minimax linear fractional programming (MLFP) problem. In this algorithm, MLFP is converted and decomposed into a series of linear programs by dividing the outer 1-dimensional space of the equivalent problem (EP) into polynomially countable intervals. To improve the computational efficiency of the algorithm, two new acceleration techniques are introduced, in which the regions in outer space where the optimal solution of EP does not exist are largely deleted. In addition, the global convergence of the proposed algorithm is summarized, and its computational complexity is illustrated to reveal that it is a fully polynomial time approximation scheme. Finally, the numerical results demonstrate that the proposed algorithm is feasible and effective. [ABSTRACT FROM AUTHOR]

This paper investigates a class of linear fractional programming (LFP) problem, which minimizes the sum of a finite number of linear fractional functions over a polyhedral region. Firstly, the equivalence problem (EP) of the LFP problem is given by a new two-stage transformation method. Secondly, considering the characteristics that the branch-and-bound algorithm can guarantee the global optimality of the solution to an optimization problem, and then based on the EP, we discuss the bounding operation, branching operation, pruning operation and rectangle-region reduction technique of this algorithm. After that, the convergence of the algorithm is proved and its computational complexity is deduced from the worst case. Finally, some experiments are reported to verify the effectiveness, feasibility and other performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of maximizing the sum of a concave–convex quadratic fractional function on a non-empty, bounded, convex quadratic feasible set, which is called the problem (QCQFP). By using a conventional semidefinite program (SDP) relaxation, QCQFP is reformulated as a class of linear fractional programming problems over the cone of positive semidefinite matrices, which we refer to these problems as SDFP. After expatiating the properties of SDFP, we transform SDFP into its equivalent problem (ESDFP) whose non-convexity is mainly reflected in the newly added nonlinear equality constraints. By relaxing these nonlinear equality constraints into linear constraints, a special SDP relaxation is generated for ESDFP. Based on these results, an effective branch-and-bound algorithm is designed, and its theoretical convergence and worst-case complexity are proved. Numerical experiments demonstrate that the proposed algorithm is effective and feasible. [ABSTRACT FROM AUTHOR]

For the minimization of the sum of linear fractions on polyhedra, it is likewise a class of linear fractional programming (LFP). In this paper, we mainly propose a new linear relaxation technique and combine the branch-and-bound algorithm framework to solve the LFP globally. It is worthwhile to mention that the branching operation of the algorithm occurs in the relatively small output space of the dimension rather than the space where the decision variable is located. When the number of linear fractions in the objective function is much lower than the dimension of the decision variable, the performance of the algorithm is better. After that, we also explain the effectiveness, feasibility, and other performances of the algorithm through numerical experiments. [ABSTRACT FROM AUTHOR]