The strategy of Restricted Simplicial Decomposition is extended to convex programs with convex constraints. The resulting algorithm can also be viewed as an extension of the (scaled) Topkis-Veinott method of feasible directions in which the master problem involves optimization over a simplex rather than the usual line search. Global convergence of the method is proven and conditions are given under which the master problem will be solved a finite number of times. Computational testing with dense quadratic problems confirms that the method dramatically improves the Topkis-Veinott algorithm and that it is competitive with the generalized reduced gradient method.
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