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Question Number 192979 by Red1ight last updated on 01/Jun/23
$$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{optimized}\:\left(\mathrm{getting}\:\mathrm{the}\:\mathrm{minimum}\right)\:\mathrm{using}\:\mathrm{backprobagation}? \\ $$$$ \\ $$$$\alpha\left({x}_{{i}} ,{y}_{{i}} ,{h}_{{i}} \right)=\left({h}_{{i}} −{x}_{{i}} \right)^{\mathrm{2}} +{y}_{{i}} ^{\mathrm{2}} \\ $$$$\beta\left({y}_{{i}} ,{h}_{{i}} \right)={y}_{{i}} {h}_{{i}} ^{\mathrm{2}} −\mathrm{2}{uy}_{{i}} {h}_{{i}} \\ $$$$\gamma\left({h}_{{i}} \right)={h}_{{i}} ^{\mathrm{4}} −\mathrm{4}{uh}_{{i}} ^{\mathrm{3}} +\mathrm{4}{u}^{\mathrm{2}} {h}_{{i}} ^{\mathrm{2}} \\ $$$$\mathrm{Cost}=\underset{{i}=\mathrm{0}} {\overset{{m}} {\sum}}\left(\mathrm{c}\alpha\left({x}_{{i}} ,{y}_{{i}} ,{h}_{{i}} \right)−\mathrm{2}{c}^{\mathrm{2}} \beta\left({y}_{{i}} ,{h}_{{i}} \right)+{c}^{\mathrm{3}} \gamma\left({h}_{{i}} \right)\right) \\ $$$$\mathrm{and}\:\mathrm{how}? \\ $$