A
| Semi-Infinite Linear Programming |
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SIP studies the optimisation problems in which the number of constraints is infinite, because it is indexed in a compact set, while the number of decision variables is finite. In the early years of our research in this line we were dedicated primarily to developing theoretical and numerical methods of feasible directions to solve the ongoing problem of SIP with linear constraints. Recently, we have been concerned about the use of such techniques in specific fuzzy mathematical programming problems.
B
| Fuzzy Mathematical Programming |
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Many practical problems in diverse areas are solved using fuzzy mathematical programming techniques. We have worked on the problem of staff planning and on the one regarding the viability of infeasible instances in LP (which can be classified as flexible scheduling problems) and the efficient allocation problem using a DEA model, which belongs to the field of possibilistic programming.
C
| Optimisation methods applied to time series prediction |
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We have developed and applied nonlinear optimisation algorithms for the calculation of specific predictions using different exponential smoothing methods, mainly in connection with the multiplicative Holt-Winters method. In the case of financial time series prediction, which appear in sales and inventory management, we have developed a computer program, SIOPRED, which enables automatic prediction for series of groups of similar properties, both individually and for product families.
At present we are interested in the validation of predictive models used to design prediction intervals
D
| Portfolio selection |
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The portfolio selection problem is about determining the optimum composition of a portfolio. We addressed this problem as a multiobjective programming problem in the context of balance between risk and return, and alternatively we have studied it as a possibilistic programming problem, where the imprecise knowledge of the returns is modelled by LR fuzzy numbers.
Recently, we used these results to develop an interactive system, CAOBA, which also incorporates other approaches to the problem and allows to automatically determine the composition of a portfolio in accordance with the desire for diversification of the investor, among other things.
