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The problem of constructing a dual cone of a convex polyhedral cone arises in many mathematical and applied researches. In the paper the method of constructing the dual cone to the acute convex polyhedral cone in R3 is proposed. The Householder transformation, creating a convex hull on the plane and projecting the point lying on the z-axis onto a corresponding face are the basic operations which we...
The problem of minimizing the maximum of two strongly convex quadratic functions on Rn is considered. It is shown that in some cases this problem is equivalent to finding the positive root of a polynomial of the degree 2n or less.
Methods of penalty functions are widely used in nonlinear programming. The idea of penalty function methods consists in reducing the problem of conditional optimization to a problem of the unconstrained optimization. Among the different approaches existing for such reduction we shall consider the method of exact penalty nondifferentiable functions. The implementation of exact penalty function methods...
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