May 13, 2006 · We show how these conditions can be used to obtain simple and unified proofs of some known results on existence of optimal solutions, and to ...

May 13, 2006 · We show that asymp- totic, retractive, horizon, and critical directions provide the basis for new set intersection theorems, new existence of ...

We show how these conditions can be used to obtain simple proofs of some known results on existence of optimal solutions, and to derive some new results, ...

critical directions provide the basis for new set intersection theorems, new existence of optimal solutions results, and simpler proofs of known theorems.

Dec 30, 2004 · We show how these conditions can be used to obtain simple proofs of some known results on existence of optimal solutions, and to derive some new ...

We show how these conditions can be used to obtain simple and unified proofs of some known results on existence of optimal solutions, and to derive some new ...

The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, ...

To prove the nonemptiness of the set of optimal solutions, we will use the Weierstrass theorem, which is stated below. Theorem 6 (Weierstrass). A continuous ...

Set Intersection Theorems and Existence of Optimal Solutions. Dimitri P. Bertsekas; Paul Tseng. OriginalPaper 13 May 2006 Pages: 287 - 314. An Extension of Sums ...

The lower semi-continuity of certain functionals on certain sets of trajectories is also proved. Existence theorems for optimal controls in ordinary and relaxed ...