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A New Scaled Secant-Type Conjugate Gradient Algorithm

Motivated by the success of Shanno’s memoryless Conjugate Gradient (CG) methods [28,29], this paper derives a new scaled quasi-Newton like CG algorithm that utilizes an update formula that is invariant to a scaling of the objective function. The computation of the search directions at each iteration is done in two steps. The computations involved are rather cheap as they merely involve a number of inner products and require extra O(n) storage requirements. The extra requirements are shown to pay off when the algorithm is numerically compared to that developed by Shanno.