Cyclic Coordinate Method IENG511 Optimization Theory NASIM SADEGH Spring 2013-14

Cyclic Coordinate Method This method uses the coordinate axes as the search directions. More specifically, the method searches along the directions d1 ,..., dn where d1 is a vector of zeros except for a 1 at the jth position. Thus, along the search direction dj, the variable x j is changed while all other variables are kept fixed.

Summary of the Cyclic Coordinate Method

Example Consider the following problem: Note that the optimal solution to this problem is (2, 1) with objective value equal to zero. Table bellow gives a summary of computations for the cyclic coordinate method starting from the initial point (0, 3). Note that at each iteration, the vectors y2 and y3 are obtained by performing a line search in the directions (1, 0) and (0, l), respectively. Also note that significant progress is made during the first few iterations, whereas much slower progress is made during later iterations. After seven iterations, the point (2.22, 1.1 l), whose objective value is 0.0023, is reached.

Convergence of the Cyclic Coordinate Method

Acceleration Step

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