Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

Minghuang Li (Beijing Normal University, China) and Fusheng Yu (Beijing Normal University, China)
DOI: 10.4018/978-1-61350-456-7.ch208
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Abstract

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.
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Preliminaries

In this section, we give some notations used in this paper and briefly introduce the related preliminary knowledge.

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