A novel chance constrained programming approach for process optimization of large-scale nonlinear dynamic systems and control under uncertainty is proposed. The stochastic property of the uncertainties is explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. This incorporates the issue of feasibility and...

The major function of dynamic networks is to sense information from the environment and process the information to the downstream. Therefore how to measure the information transmission ability of a dynamic network is an important topic to evaluate network performance. However, the dynamic behavior of a dynamic network is complex and, despite knowledge of network components, interactions and noi...

Probability-one homotopy algorithms are a class of methods for solving nonlinear systems of equations that, under mild assumptions, are globally convergent for a wide range of problems in science and engineering. Convergence theory, robust numerical algorithms, and production quality mathematical software exist for general nonlinear systems of equations, and special cases such as Brouwer fixed ...

In this paper, a nonlinear phase finite impulse response (FIR) filter is designed without imposing a desired phase response. The maximum passband group delay of the filter is minimized subject to a positivity constraint on the passband group delay response of the filter as well as a specification on the maximum absolute difference between the desired magnitude square response and the designed m...

The paper proposes two Nonlinear Model Predictive Control schemes that uncover a synergistic relationship between on-line receding horizon style computation and Particle Swarm Optimization, thus benefiting from both the performance advantages of on-line computation and the desirable properties of Particle Swarm Optimization. After developing these techniques for the unconstrained nonlinear opti...

This article proposes a new approach for centralized path planning of multiple aircraft in presence of the obstacle-laden environment under low flying rules. The problem considers as a unified nonlinear constraint optimization problem. The minimum time and control investigate as the cost functions and the maximum velocity and power consider as the constraints. The pseudospectral method applies ...

In this report, we investigate the relation between supersymmetry (twisted and untwisted) and geometry for two dimensional σ model with target spaces of arbitrary signature, and Lorentzian or Euclidean world sheets. It can be shown that the number of allowed supersymmetry is constrained purely by the geometric considerations. The possible geometries are classified according to properties of the...

When solving the general smooth nonlinear optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy ǫ can be obtained by a second-order method using cubic regularization in at most O(ǫ) problem-functions evaluations, the same order bound as in the unconstrained case. This result is obtained by first showing that the same result ...

This paper presents a problem-independent framework that uni es various mechanisms for solving discrete constrained nonlinear programming (NLP) problems whose functions are not necessarily di erentiable and continuous. The framework is based on the rst-order necessary and su cient conditions in the theory of discrete constrained optimization using Lagrange multipliers. It implements the search ...