1. The optimality conditions of saddle points, weakly duality theorem, strong duality theorem and converse duality theorem are obtained under convexity assumptions.

2. In Optimality Theory, grammar consists of a set of universal and violable constraints.

3. This paper describes an problem of optimality for constraint nonlinear programming with mixed discrete variable.

4. It is discovered that convergence rate with asymptotical optimality for the proposed EB test can arbitrarily approach to 1 under certain conditions.

5. Through all the optimality sufficient conditions and duality problems were discussed on basis of generalized convexity.

6. With principle of optimality and finite element analysis, optimized result was get for oil room.

7. In this article, we introduce the principle of optimality in dynamic programming and some methods for solving certain simple variable and multi-variable problems.

8. Using the theorem, the optimality necessary conditions and sufficient conditions for the vector optimization problems with generalized inequality constraint are obtained.

9. Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.

10. It is important to realize the Pareto Optimality of credit allocation in regions.

11. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory.

12. The principle of optimality under condition is proposed, so the dynamic programming is extended to the optimization of the system with delay.

13. Finally, a heuristic search for the optimality would be performed under the constraints.

14. Based on the principle of optimality, a dynamic programming algorithm of minimal transfer times for a viable route was designed and this could be used to determine the upper bound.

15. And finally, the optimality conditions are obtained for set-valued vector optimization problems in a sense of weak efficient solutions by applying the theorem.

16. The necessary conditions for optimality were derived by calculus of variations.

17. Equivalent condition for optimality are obtained, and explicit solution leading to feedback formulae are derived for special utility functions and for deterministic coefficients.

18. The drawbacks of simulated evolutionary algorithms are that the global optimality can not be always guaranteed because of randomicity and premature con vergence.

19. Optimization of ownshipmaneuver strategies for better tracking results is studied in this paper, here the optimality criteria is maximizing the degree of observability ofthe system.

20. This dissertation is devoted to the study of sup-type function on non-compact set and the first-order optimality conditions for generalized semi-infinite programming with inequality constraints.

21. The experimental results show that this method has the advantages of robustness, global optimality and high convergent speed and it is feasible for optical flow estimation of nonrigid body.

22. Some important properties of multifacility location models are to be dealt with, and an optimality condition for multifacility location problem on a closed convex set is put forward.

23. A new two-step control method based on the principle of optimality is proposed for the gravity-flow in open channel system.

24. In this article, we will study the multi-dimensional multistage fuzzy optimal control question, which mainly draw support from the Bellman optimality principle.

25. Besides, we give a polynomial algorithm to solve the one group case to optimality.

26. The optimization algorithm for the relaxed subproblem is constructed by virtue of the optimality function and the convergence is proved.

27. An experiment shows that the method has advantage in performance and outputted node number, and moreover, when the space of the main memory is changed, the method still has notable optimality.

28. This paper solves some special estimating value problems of double integral with the help of the optimality principle and graphical solution of the linear programming.

28. Wish you will love and make progress everyday!

29. By virtue of this minimax problem as well as the directionally differentiable property of the functions in every subproblem, the first-order optimality conditions are obtained.

30. In this paper, an iterative formula to solving non-degenerate LP to optimality is given.

31. Further, an implicit iterative algorithm for the design variables is also established based on SIMP interpolation scheme and optimality criteria method.

32. The optimality conditions for multiobjective semi - infinite programming with semilocally convex functions are given.

33. Optimality conditions for vector optimization problem to attain strictly efficient solutions are considered in the paper.

34. Under the conditions of Partial ic-convex like Maps, optimality necessary conditions of weak efficient solutions for vector optimization problems with equality and inequality constraints are obtained.

35. By the alternative theorem, the optimality conditions of vector extremum problems with generalized inequality constraint are established in linear space.http://

36. On the basis of Pareto efficiency, the shadow price is defined as the marginal value of resources and goods in the state of Pareto optimality.

37. As an extension, the branch-and-bound algorithm put forward in this paper can solve this kind of general project scheduling problems with optimality .

38. In this paper we prove uniqueness and existence of the optimal fission cross section, and give the optimality condition.

39. Under the given condition, we have proved the existence and uniqueness of the minimum norm scattering fission cross section control element , and have given its corresponding optimality conditions.

40. The theoretic fundamentals for the commonly used biplane truncation algorithm is expounded, and its sub- optimality is pointed out.

41. The necessary conditions for optimality were derived calculus of variations.