In this paper, the multivariate fractional trading ansatz of money management from Vince (Vince 1990) is discussed. In particular, we prove existence and uniqueness of an “optimal f ” of the respective optimization problem under reasonable assumptions on the trade return matrix. This result generalizes a similar result for the univariate fractional trading ansatz. Furthermore, our result guaran...

⎯In this paper, we propose a model and a solution procedure to minimize the cost associated with mass customizing consumer products in the presence of multivariate constraints. Three algorithms based on enumeration, steepest descent and Lagrange relaxation are used to solve the non-linear optimization problem and their performance is evaluated with numerical experiments. The sufficient and nece...

NLCertify is a software package for handling formal certification of nonlinear inequalities involving transcendental multivariate functions. The tool exploits sparse semialgebraic optimization techniques with approximation methods for transcendental functions, as well as formal features. Given a box and a transcendental multivariate function as input, NLCertify provides OCaml libraries that pro...

The madness package provides a class for automatic differentiation of ‘multivariate’ operations via forward accumulation. By ‘multivariate,’ we mean the class computes the derivative of a vector or matrix or multidimensional array (or scalar) with respect to a scalar, vector, matrix, or multidimensional array. The primary intended use of this class is to support the multivariate delta method fo...

The optimization of computationally expensive objective functions requires approximations that preserve the global properties of the function under investigation. The RSM approach of using multivariate polynomials of degree two can only preserve the local properties of a given function and is therefore not well-suited for global optimization tasks. In this paper we discuss generalized Bernstein...

In this article, we apply the mean-expected tail loss (ETL) portfolio optimization to the consensus temporary earnings forecasting (CTEF) data from global equities. The time series model with multivariate normal tempered stable (MNTS) innovations is used to generate the out-of-sample scenarios for the portfolio optimization. We find that (1) the CTEF variable continues to be of value in portfol...

Mixed-integer optimization problems arise in various application fields, such as chemical engineering and the optimization of medical image processing pipelines. Stochastic optimization algorithms, such as evolution strategies and estimation of distribution algorithms, can be used as solution methods for solving these problems approximately. Especially for real-world problems they often prove t...

ultivariate stochastic optimization plays a major role in the analysis and control of many engineering systems. In almost all real-world optimization problems, it is necessary to use a mathematical algorithm that iteratively seeks out the solution because an analytical (closed-form) solution is rarely available. In this spirit, the “simultaneous perturbation stochastic approximation (SPSA)” met...

ultivariate stochastic optimization plays a major role in the analysis and control of many engineering systems. In almost all real-world optimization problems, it is necessary to use a mathematical algorithm that iteratively seeks out the solution because an analytical (closed-form) solution is rarely available. In this spirit, the “simultaneous perturbation stochastic approximation (SPSA)” met...