Convexification of nonconvex functions and application to minimum and maximum principles for nonconvex sets
نویسندگان
چکیده
منابع مشابه
Convexification Procedures and Decomposition Methods for Nonconvex Optimization Problems 1
In order for primal-dual methods to be applicable to a constrained minimization problem, it is necessary that restrictive convexity conditions are satisfied. In this paper, we consider a procedure by means of which a nonconvex problem is convexified and transformed into one which can be solved with the aid of primal-dual methods. Under this transformation, separability of the type necessary for...
متن کاملRecession Cones of Nonconvex Sets and Increasing Functions
In this article a local characterization theorem is given for closed sets in a linear topological space that have recession cones with nonempty interior. This theorem is then used to characterize the class of upper semicontinuous increasing functions defined on closed E% -recessional subsets of Ed.
متن کاملTransversality and Alternating Projections for Nonconvex Sets
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. When the two sets are semi-algebraic and bounded, but not necessarily transversal, we nonetheless prove subsequence convergence.
متن کاملCutting-Planes for Optimization of Convex Functions over Nonconvex Sets
We derive linear inequality characterizations for sets of the form conv{(x, q) ∈ R×R : q ≥ Q(x), x ∈ R − int(P )} where Q is convex and differentiable and P ⊂ R. We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite quadratic and P is a polyhedron or an ellips...
متن کاملStrong formulations for convex functions over nonconvex sets
Preliminaries. Several important classes of optimization problems include nonlinearities in the objective or constraints. Often this results in nonconvexities and a current research thrust addresses the computation of global bounds and exact solution techniques for such problems. The field is not new; one of the earliest results is the characterization of the convex hull of a box-constrained bi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1996
ISSN: 0898-1221
DOI: 10.1016/0898-1221(96)00016-8