The space transformation technique in mathematical programming
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The present paper is devoted to the application of the space transformation technique for solving linear and nonlinear programming problems. By using a surjective mapping the initial constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem we use the generalized gradient-projection method and Newton’s method. After inverse transformation to the initial space we obtain the family of numerical methods for solving optimization problems with equality and inequality constraints. In the linear programming case after some simplification and after choosing a particular exponential transformation function we obtain from the proposed methods the well-known primal-dual interior point linear programming algorithm and the so-called “variation of Kermarkar’s algorithm”.
Key wordsconstrained minimum problem space transformation gradient-projection method Newton’s method linear programming nonlinear programming interior point technique primal-dual method barrier function
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