In this paper we analyze the rate of local convergence of the Newton primal-dual interior-point method when the iterates are kept strictly feasible with respect to the inequality constraints. It is shown under the classical conditions that the rate is q-quadratic when the functions associated to the inequality constraints define a locally concave feasible region. … Read more
This paper considers strategies for selecting the barrier parameter at every iteration of an interior-point method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra’s probing procedure, outperform static strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the … Read more
Augmented Lagrangian methods with general lower-level constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lower-level type. Two methods of this class are introduced and analyzed. Inexact resolution of the lower-level constrained subproblems is considered. Global convergence is proved … Read more
Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) entities interacting locally with their environment cause coherent functional global patterns to emerge. SI provides a basis with wich it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model. To … Read more
Swarm Intelligence (SI) is the property of a system whereby the collective behaviors of (unsophisticated) entities interacting locally with their environment cause coherent functional global patterns to emerge. SI provides a basis with wich it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model. In … Read more
The DIRECT algorithm was motivated by a modification to Lipschitzian optimization. The algorithm begins its search by sampling the objective function at the midpoint of an interval, where this function attains its lowest value, and then divides this interval by trisecting it. One of its weakness is that if a global minimum lies at the … Read more
This note, attempts to further Pan’s second-order quasi-Newton methods(\cite{panqn}). To complement the numerical implementation, the linear convergence of a rank-one second-order update and the least change property are presented. Citation 1,Department of Mathematics, Southeast University, Nanjing, 210096, P.R.China.
In this paper we study the behavior of Convex Quadratic Optimization problems when variation occurs simultaneously in the right-hand side vector of the constraints and in the coefficient vector of the linear term in the objective function. It is proven that the optimal value function is piecewise-quadratic. The concepts of transition point and invariancy interval … Read more
We formulate an optimal control problem of magnetization in a ferromagnet as a mathematical program with evolutionary equilibrium constraints. The evolutionary nature of the equilibrium is due to the hysteresis behavior of the respective magnetization process. To solve the problem numerically, we adapted the implicit programming technique. The adjoint equations, needed to compute the subgradients … Read more
We present a method to compute the implied volatility of American options as a mathematical program with equilibrium constraints. The formulation we present is new, as are the convergence results we prove. The algorithm holds the promise of being practical to implement, and we demonstrate some preliminary numerical results to this end. Citation Princeton University … Read more