Particle swarm optimization algorithm based on parametric equation method to handle equality constraints;

The Descending Dimension Algorithm by a Nonlinear System of Equations of the Programming Problems with Equality Constraints;

In the paper, equality constraints after networks distributed are included into objective function with Lagrange multiplier based on PMUs, so the problem of the distributed state estimation is changed into optimization problem with equality constraints, realized the distributed paral.

Implying a multivariate equality constraint in switching function, a genetic algorithm (GA) based improved mathematical model for fault location of distribution network is built.

For a class of networked control systems(NCS) with equality constraint,this paper addresses the problem of designing controller,sampling period and the maximum allowable delay bound(MADB).

A multivariable equality constraint condition is hidden in switching functions through different equivalent transformations.

For the cases of process model uncertainties and equipment leakage,a data reconciliation method with inequality constraints and its application examples were presented.

Inequality constraints were handled with the similar method as their equality counterparts in Lagrange multiplier method,while the multipliers associated with inequality constraints were written as a positive definite function of the originally-defined multipliers.

A method for incorporating linear state inequality constraints in a Kalman filter is proposed and applied to turbofan engine health estimation.

Aiming at the nonlinear optimization problems with inequality restriction,we analyzed why the convergence speed of the traditional complex shape arithmetic was slow.

For the growth curve model with respect to inequality restriction:Y=XBZ+ε,ε~→～(0,σ~2VI),tr(NB)≥0,this paper gives the definition of general admissibility of linear estimates under the matrix loss function(d(Y)-KBL)(d(Y)-KBL) .

In this thesis,the admissibility and general admissibility of linear estimators in growth curve model with respect to inequality restriction are considered.

A new algorithm for solving inequality constraint optimization problem;

This paper presents some approximate algorithms for minimax nonlinear programs with inequality constraints by using maximum entropy method and algorithms relevant to nonlinear programming with inequality constraints,and convergence theorems concerning these algorithms are given.

To inequality constraints, a check procedure and a penalty function procedure are proposed, and equality constraints are dealt with by a procedure of solving equations in which tear equations may be converged by an iterating way or a penalty function way.

An interior affine scaling subspace trust region method for nonlinear optimizations subject to linear inequality constraints;

An interior affine scaling indefinite dogleg path algorithm for nonlinear optimizations subject to linear inequality constraints;

Interior affine scaling curvilinear path algorithm for nonlinear optimizations subject to linear inequality constraints;