Mean–variance portfolio optimal problem under concave transaction cost

The multiplicative weights update algorithm for mixed integer nonlinear programming: theory, applications, and limitations

“…Problem (3.42) generalizes the usual portfolio problem with concave transaction costs already considered in the literature (see, e.g., Konno and Wijayanayake [148] and Xue et al [245]). To the best of our knowledge, this is the first time this kind of portfolio problems is addressed in its entirely.…”

DC programming approach for portfolio optimization under step increasing transaction costs

“…The net return is the expected rate of return of the portfolio minus the transaction cost. The inclusion of transaction costs is an essential element of any realistic portfolio optimization, and portfolio selection with transaction costs has received considerable research attention in recent years [1,5,6,8,9,13,25].…”

Export diversification through resource-based industrialization: The case of natural gas

“…The procedure continues by partitioning the subset that corresponds to the largest maxima and again maximizing the convex relaxation to the original problem over each of the resulting subsets. As proved in Xue et al (2006), this procedure provides an efficient computational Note: NA indicates that the solver failed to provide a converged solution within the allotted maximum CPU time (30,600.00 s). The relevant computer specifications are: AMD Turion 64X2 TL-60, 2.00 GHz, 2 GB RAM, 32-bit OS.…”

“…The relaxed problem is a linearly constrained, convex, quadratic programming problem and its solution provides both a lower bound (the value of the original objective function at that point) and an upper bound (the value of the relaxed objective function at that point) for the optimal objective value of the original problem (Xue and Xu, 2005). Using this framework, a branch and bound scheme can be applied to minimize the difference between these two bounds (see Xue et al, 2006). This scheme is aimed at refining the quality of the outer approximation by: (i) generating successive partitions of the initial rectangle into rectangular subsets, (ii) redefining the linear envelopes of the univariate cost functions over each of these subsets, (iii) solving the relaxed models, and (iv) recording the respective maxima.…”