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Consider the Following Discrete Nonlinear Programming Problem

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Consider the following discrete nonlinear programming problem.Maximize Z = Consider the following discrete nonlinear programming problem.Maximize Z = ,subject to x<sub>1</sub> + x<sub>2</sub> ≤ 0.75 and each variable is restricted to the values: . (a)Reformulate this problem as a pure binary integer linear programming problem. (b)Use the following outline in designing the main features of a branch-and-bound algorithm for solving this problem (and similar problems)directly without reformulation.(1)Specify the tightest possible nonlinear programming relaxation that has only continuous variables,and so can be solved efficiently by nonlinear programming techniques.(2)Specify the fathoming tests.(3)Specify a branching procedure that involves specifying two ranges of values for a single variable. ,subject to x1 + x2 ≤ 0.75 and each variable is restricted to the values: Consider the following discrete nonlinear programming problem.Maximize Z = ,subject to x<sub>1</sub> + x<sub>2</sub> ≤ 0.75 and each variable is restricted to the values: . (a)Reformulate this problem as a pure binary integer linear programming problem. (b)Use the following outline in designing the main features of a branch-and-bound algorithm for solving this problem (and similar problems)directly without reformulation.(1)Specify the tightest possible nonlinear programming relaxation that has only continuous variables,and so can be solved efficiently by nonlinear programming techniques.(2)Specify the fathoming tests.(3)Specify a branching procedure that involves specifying two ranges of values for a single variable. .
(a)Reformulate this problem as a pure binary integer linear programming problem.
(b)Use the following outline in designing the main features of a branch-and-bound algorithm for solving this problem (and similar problems)directly without reformulation.(1)Specify the tightest possible nonlinear programming relaxation that has only continuous variables,and so can be solved efficiently by nonlinear programming techniques.(2)Specify the fathoming tests.(3)Specify a branching procedure that involves specifying two ranges of values for a single variable.

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(a)We define the binary variable yi...

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