### Xiaoling Sun (Shanghai University, P.R. China)

#### Convexification, concavification and monotonization in global optimization

*Monday 13 December 1999 at 15.30, JCMB 6324*

##### Abstract

In this talk, we will present a transformation method to convert a
general nonconvex optimization problem into an equivalent better-structured
nonconvex optimization problem, e.g., a concave optimization problem or a D.C.
programming problem, thus facilitating the search of a global optimum by using
the existing methods in concave minimization and D.C. programming. We first
show that a monotone optimization problem (with a monotone objective function
and monotone constraints) can be transformed into a concave minimization
problem over a convex set or a D.C. programming problem via p-th power
transformation. We then prove that a general nonconvex minimization problem
over a simplex can always be reduced to a monotone optimization problem,
thus a concave minimization problem or a D.C. programming problem.

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