Linhai He

Unified steerable phase I-phase II method of feasible directions for semi-infinite optimization

In this paper, we complete a cycle in the construction of methods of feasible directions for solving semi-infinite constrained optimization problems. Earlier phase I-phase II methods of feasible directions used one search direction rule in all of ℝn with two stepsize rules, one for feasible points and one for infeasible points. The algorithm presented in this paper uses both a single search direction rule and a single stepsize rule in all of ℝn. In addition, the new algorithm incorporates a steering parameter which can be used to control the speed with which feasibility is achieved. The new algorithm is simpler to analyze and performs somewhat better than existing, first order, phase I-phase II methods. The new algorithm is globally convergent, with linear rate.

Adaptive Quality of Service for a Mobile Ad Hoc Network

This paper presents a QoS routing system for MANET supporting multiple traffic classes. The system takes into consideration clustering and channel allocation. Simulation experiments show that our algorithms are convergent. The system also yields a higher total throughput compared to the case in which every interface uses the same channel.

Finite-termination schemes for solving semi-infinite satisfying problems

The problem of finding a parameter which satisfies a set of specifications in inequality form is sometimes referred to as the satisfycing problem. We present a family of methods for solving, in a finite number of iterations, satisfycing problems stated in the form of semi-infinite inequalities. These methods range from adaptive uniform discretization methods to outer approximation methods.

Stochastic approximation and transaction-level model for IP network design

We investigate the use of simulation and transaction level models for transmission control protocol (TCP) in Internet Protocol (IP) network design. More specifically, we focus on the transaction level dynamics of TCP and approximate it by max-min fair sharing. Based on this model, we formulate a network dimensioning problem as a nonlinear constrained optimization problem. The constraints and their gradients, which do not have analytical forms, are estimated through fluid simulation of the transaction-level model of TCP. The problem is solved by a gradient descent type of algorithm, with additional heuristics based techniques to improve its convergence. The performance of the proposed algorithm is evaluated through experimental studies on example networks. Results show that the methods are promising and can help the design of networks.

Rate preserving discretization strategies for semi-infinite programming and optimal control

Discretization of semi-infinite programming and optimal control problems is addressed. Three sets of discretization refinement rules are presented: (i) for unconstrained semi-infinite minimax problems; (ii) for constrained semi-infinite problems, and (iii) for unconstrained optimal control problems. These rules are built into a master algorithm which calls certain linearly converging algorithms for finite-dimensional, finitely described optimization problems. The discretization refinement rules ensure that the sequences constructed by the overall scheme converge to a solution of the original problem with the same rate constant as applied for the finite-dimensional, finitely described approximations. Hence the resulting scheme is more efficient than fixed discretization.<<ETX>>