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- W1963561672 abstract "Abstract A polynomial programming problem is a nonlinear programming problem where the objective function, inequality constraints and equality constraints all consist of polynomial functions. The necessary optimality conditions for such a problem can be formulated as a polynomial system of equations, among whose zeros the global optimum must lie. This note applies the theory of multi-homogeneous (also called m-homogeneous ) polynomials and recent homotopy algorithms to the polynomial system formulation of the necessary optimality conditions, significantly reducing the work of a naive homotopy approach. The m -homogeneous homotopy approach, providing the global optimum, is practical for small problems. For example, the geometric modeling problem of finding the distance between two polynomial surfaces is a polynomial programming problem. The theory is illustrated in the last section by this geometric modeling problem and a prototype structural design problem." @default.
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- W1963561672 date "1992-12-01" @default.
- W1963561672 modified "2023-09-28" @default.
- W1963561672 title "Polynomial programming using multi- homogeneous polynomial continuation" @default.
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- W1963561672 doi "https://doi.org/10.1016/0377-0427(92)90022-p" @default.
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