On Nonlinear Inverse Problems of Heat Transfer with Radiation Boundary Conditions: Application to Dehydration of Gypsum Plasterboards Exposed to Fire

Table 1

Method	Notation	Descent direction	Parameter
Gradient	Grad	𝑑^(𝑘)=−𝑔^(𝑘)	—
Fletcher-Reeves CGM	CGFR	𝑑^(𝑘)=−𝑔^(𝑘)+𝛽𝑘−1𝑑^(𝑘−1)	𝛽𝑘−1=𝑔^(𝑘)2𝑔^(𝑘−1)2
Polak-Ribieres CGM	CGPR	𝑑^(𝑘)=−𝑔^(𝑘)+𝛽𝑘−1𝑑^(𝑘−1)	𝛽𝑘−1=𝑔^(𝑘)−𝑔^(𝑘−1);𝑔^(𝑘)𝑔^(𝑘−1)2
Hestenes-Stiefel CGM	CGHS	𝑑^(𝑘)=−𝑔^(𝑘)+𝛽𝑘−1𝑑^(𝑘−1)	𝛽𝑘−1=𝑔^(𝑘);𝑔^(𝑘)−𝑔^(𝑘−1)𝑑^(𝑘−1);𝑔^(𝑘)−𝑔^(𝑘−1)
Dai-Yuan CGM	CGDY	𝑑^(𝑘)=−𝑔^(𝑘)+𝛽𝑘−1𝑑^(𝑘−1)	𝛽𝑘−1=𝑔^(𝑘)2𝑑^(𝑘−1);𝑔^(𝑘)−𝑔^(𝑘−1)