**:** . .
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**:** 43
**:**
**:** 2013
**:** . . , 2: / . 43. .: , 2013. .95-123.

** :** , , ,

** (.):** nonlinear programming, matrix inequalities, polynomial inequalities, moment theory

**:** . , , .

** (.):** We investigate multidimensional optimization problems with polynomial objective function and polynomial matrix inequality constraints and suggest a transformation of the moment-theory-based solution technique. It allows reducing significantly the computational complexity while keeping the ability to solve the problems of the class under consideration.

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