An Algorithm for Separable Piecewise Convex Programming Problems.
TEXAS UNIV AUSTIN CENTER FOR CYBERNETIC STUDIES
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The author presents a branch and bound algorithm to solve mathematical programming problems of the form Find x x1,...,xn to minimize the summation of Phisub i 0x sub i subject to x belongs to G, l or x or L, and the summation of Phisub i j x sub i or O, j 1,...,m. With l l1,...,ln and L L1,...,Ln, each Phi sub i j is is assumed to be lower semicontinuous and piecewise convex on the finite interval liLi. Gis assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems these correspond to successive partitions of the set C the setxl or x or L on the basis of the piecewise convexity of the problem functions Phi sub i. Computational considerations are discussed, and an illustrative example is presented. Author
- Operations Research