2018/02/27 by Elif Garajová, Garajová, Elif, Milan Hladík +3 · 1 citation
Computer Science · Decision Sciences · Engineering · #FOS: Mathematics #Numerical Methods and Algorithms #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Water resources management and optimization
paper · pdf · doi:10.48550/arxiv.1802.09872
openalex publication_date 2018/02/27 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28
Interval linear programming provides a tool for solving real-world\noptimization problems under interval-valued uncertainty. Instead of\napproximating or estimating crisp input data, the coefficients of an interval\nprogram may perturb independently within the given lower and upper bounds.\nHowever, contrarily to classical linear programming, an interval program cannot\nalways be converted into a desired form without affecting its properties, due\nto the so-called dependency problem.\n In this paper, we discuss the common transformations used in linear\nprogramming, such as imposing non-negativity on free variables or splitting\nequations into inequalities, and their effects on interval programs.\nSpecifically, we examine changes in the set of all optimal solutions, optimal\nvalues and the optimal value range. Since some of the considered properties do\nnot holds in the general case, we also study a special class of interval\nprograms, in which uncertainty only affects the objective function and the\nright-hand-side vector. For this class, we obtain stronger results.\n