FORMULATION OF CONCAVE-CONVEX FRACTIONAL PROGRAMMING MODEL FOR BANK PORTFOLIO SELECTIONS

In this paper, a concave-convex fractional programming model for bank portfolio selections is formulated. We have transformed the model into a concave quadratic programming problem and developed a technique for its solution. A real life application of the model is performed with twelve banks in Nigeria. The optimal solution determined by the proportion of investment to be made by an investor in each bank in order to maximize the expected returns at minimum risk is highlighted. However, the computational results show that the proposed model can generate a favourable portfolio strategy according to the investor’s satisfactory degree.  The trade-off curve also indicates the amount of risk that is commensurate with a particular expected return. Key words: concave-convex, fractional programming problem, optimization, transformatio

Global Minimization for Generalized Polynomial Fractional Program

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem (P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of (P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of (P) does not exist, which can be seen as an accelerating device for the solution algorithm of (P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem (P) provided that the number of variables is not too large

Minimization of Sum Inverse Energy Efficiency for Multiple Base Station Systems

A sum inverse energy efficiency (SIEE) minimization problem is solved. Compared with conventional sum energy efficiency (EE) maximization problems, minimizing SIEE achieves a better fairness. The paper begins by proposing a framework for solving sum-fraction minimization (SFMin) problems, then uses a novel transform to solve the SIEE minimization problem in a multiple base station (BS) system. After the reformulation into a multi-convex problem, the alternating direction method of multipliers (ADMM) is used to further simplify the problem. Numerical results confirm the efficiency of the transform and the fairness improvement of the SIEE minimization. Simulation results show that the algorithm convergences fast and the ADMM method is efficient

Optimising portfolio diversification and dimensionality

A new framework for portfolio diversification is introduced which goes beyond the classical mean-variance approach and portfolio allocation strategies such as risk parity. It is based on a novel concept called portfolio dimensionality that connects diversification to the non-Gaussianity of portfolio returns and can typically be defined in terms of the ratio of risk measures which are homogenous functions of equal degree. The latter arises naturally due to our requirement that diversification measures should be leverage invariant. We introduce this new framework and argue the benefits relative to existing measures of diversification in the literature, before addressing the question of optimizing diversification or, equivalently, dimensionality. Maximising portfolio dimensionality leads to highly non-trivial optimization problems with objective functions which are typically non-convex and potentially have multiple local optima. Two complementary global optimization algorithms are thus presented. For problems of moderate size and more akin to asset allocation problems, a deterministic Branch and Bound algorithm is developed, whereas for problems of larger size a stochastic global optimization algorithm based on Gradient Langevin Dynamics is given. We demonstrate analytically and through numerical experiments that the framework reflects the desired properties often discussed in the literature