Using the Langrage
function and kernel K([x.sub.m], [x.sub.n]) [less than or equal to] [phi]([x.sub.m]), [phi]([x.sub.n]) > 0, we could get the dual form of problem (2):
We set the robot's execution time constraint t = 60s, the initial Langrage
multiplier [[lambda].sup.0] = (0, 0,0), the initial penalty factor [r.sup.0] = (1000,1000, ..., 1000), the convergence accuracy [epsilon] = 0.0001, the constraint error accuracy [[epsilon].sub.g] = 0.0001, the Lagrange multiplier update maximal times [v.sub.max] = 100, the maximum number of iterations in the CPSO [k.sub.max] = 100, the swarm particle number [N.sub.d,max] = 40, and the elastic coefficient [alpha] = 100.
The result of Jarque-Bera (JB) normality test show that at 5% alpha value, the value of Langrage
Multiplier (LM) statistics is 0.214118 with a corresponding probability value of 0.898472.
Next, a Breusch-Pagan Langrage
Multiplier test was performed to know whether pooled OLS or random effect panel model shall be used.
In this case, we follow Tichy  and use the Breusch-Pagan Langrage
An in-depth examination of these results using the Langrage
Multiplier test (LM test) showed that many changes in model parameters were suggested in order to reduce model discrepancy, reduce the chi-square value, and, therefore, achieve adequate RMSEA and SRMR indexes (for more information on the mathematical approach behind the SRMR and RMSEA, see Brown, 2006).
Accordingly, the items that presented Langrage
Multipliers (LM) > 11 (p < 0.001), suggesting correlation between errors of measurement, were excluded.
t = y + b * j = f (0) + [f.sup.-] (0) j mod q by using Langrage
equation to [d.sub.i].
Modification indices were calculated (Multiplier Langrage
), which indicated that the model improved significantly when direct connections between task climate and discipline, and ego climate and indiscipline were considered.