Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

Multi-criteria decision-making method with incomplete certain information based on intuitionistic fuzzy number

Abstract: For multi-criteria decision making problems,in which the information on criteria's weights is incomplete and the criteria values are intuitionistic trapezoidal fuzzy numbers,a method of multi-criteria decision-making with incomplete certain information based on intuitionistic trapezoidal fuzzy number is proposed.By using the incomplete certain information of criteria weight coefficient,the optimized nonlinear programming based on Hamming distance between integrated intuitionisitc trapezoidal fuzzy number of each alternative and ideal-solution and non-ideal solution is constructed.By solving the nonlinear programming,the optimized criteria weight coefficients are attained.Then,the relative closeness to the ideal solution of alternative is obtained.The ranking of the alternatives set can be obtained by comparing the relative closeness of alternatives.Finally,an example analysis shows the feasibility and effectiveness of the method.

Stability of queueing networks and scheduling policies

Abstract: Usually, the stability of queueing networks is established by explicitly determining the invariant distribution. However, except for product form queueing networks, such explicit solutions are rare. We develop here a programmatic procedure for establishing the stability of queueing networks and scheduling policies. The method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a Lyapunov function. If the underlying system is Markovian, our method establishes not only positive recurrence and the existence of a steady-state probability distribution, but also the geometric convergence of an exponential moment. We illustrate this method on several example problems. For an open re-entrant line, we show that all stationary nonidling policies are stable for all load factors less than one. This includes the well known first-come-first-served (FCFS) policy. We determine a subset of the stability region for the Dai-Wang example (1991), for which they have shown that the Brownian approximation does not hold. In another re-entrant line, we show that the last-buffer-first-served (LBFS) and first-buffer-first-served (FBFS) policies are stable for all load factors less than one. Finally, for the Rybko-Stolyar example (1992), for which a subset of the instability region has been determined by them under a certain buffer priority policy, we determine a subset of the stability region. >

A tolerant algorithm for linearly constrained optimization calculations

Abstract: Two extreme techniques when choosing a search direction in a linearly constrained optimization calculation are to take account of all the constraints or to use an active set method that satisfies selected constraints as equations, the remaining constraints being ignored. We prefer an intermediate method that treats all inequality constraints with “small” residuals as inequalities with zero right hand sides and that disregards the other inequality conditions. Thus the step along the search direction is not restricted by any constraints with small residuals, which can help efficiency greatly, particularly when some constraints are nearly degenerate. We study the implementation, convergence properties and performance of an algorithm that employs this idea. The implementation considerations include the choice and automatic adjustment of the tolerance that defines the “small” residuals, the calculation of the search directions, and the updating of second derivative approximations. The main convergence theorem imposes no conditions on the constraints except for boundedness of the feasible region. The numerical results indicate that a Fortran implementation of our algorithm is much more reliable than the software that was tested by Hock and Schittkowski (1981). Therefore the algorithm seems to be very suitable for general use, and it is particularly appropriate for semi-infinite programming calculations that have many linear constraints that come from discretizations of continua.