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.

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.

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.

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;

A strongly subfeasible directions method for solving nonlinear inequality constrained optimization problems is presented by using the generalized gradient projection.

In this paper,a feasible interior point method is proposed for solving inequality constrained optimization problem.

In this paper,a new QP-free feasible method is proposed for solving inequality constrained optimization problems,by a new piecewise linear NCP functions.