The optimal value function (c, b)->phi(c, b) of the quadratic program min {1/2x(T) Dx + c(T) x: Ax >= b}, where D is an element of R-S(nxn) is a given symmetric matrix, A is an element of R-mxn a given matrix, c...
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The optimal value function (c, b)->phi(c, b) of the quadratic program min {1/2x(T) Dx + c(T) x: Ax >= b}, where D is an element of R-S(nxn) is a given symmetric matrix, A is an element of R-mxn a given matrix, c is an element of R-n and b is an element of R-m are the linear perturbations, is considered. It is proved that phi is directionally differentiable at any point (w) over bar=((c) over bar, (b) over bar) in its effective domain W:={w = (c, b) is an element of R-n x R-m: -infinityquadratic on W. The preceding (unpublished) example of Matte is also discussed.
An algorithm for solving a linear multiplicative programmingproblem (referred to as LMP) is proposed. LMP minimizes the product of two linear functions subject to general linear constraints. The product of two linear...
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An algorithm for solving a linear multiplicative programmingproblem (referred to as LMP) is proposed. LMP minimizes the product of two linear functions subject to general linear constraints. The product of two linear functions is a typical non-convex function, so that it can have multiple local minima. It is shown, however, that LMP can be solved efficiently by the combination of the parametric simplex method and any standard convex minimization procedure. The computational results indicate that the amount of computation is not much different from that of solving linear programs of the same size. In addition, the method proposed for LMP can be extended to a convex multiplicative programmingproblem (CM P), which minimizes the product of two convex functions under convex constraints.
Finitely convergent algorithms for solving rank two and three bilinear programmingproblems are proposed. A rank k bilinear programmingproblem is a nonconvex quadratic programming problem with the following structure...
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