Where\(\left({\overset{\overline{}}{x}}_{k},\ {\overset{\overline{}}{y}}_{k}\ ,{\overset{\overline{}}{M}}_{k},\ {\overset{\overline{}}{v}}_{\text{mk}}\right)\)for \(k=0,1,\ldots,N\) are the variables of the problem (34)-(35). The
pointwise approximate optimal solutions\(\left({\overset{\overline{}}{x^{*}}}_{k},\ {\overset{\overline{}}{y^{*}}}_{k}\ ,{\overset{\overline{}}{M^{*}}}_{k},\ {\overset{\overline{}}{v^{*}}}_{\text{mk}}\right)\)for \(k=0,1,\ldots,N\) are obtained by solving the NLP problem
(34)-(35). Moreover, the continuous approximate optimal solutions for
the OC problem (21)-(23) is derived by replacing these approximations in
(28) as follows