Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

GLOBAL CONVERGENCE OF A TRUST REGION ALGORITHM USING INEXACT GRADIENT FOR EQUALITY-CONSTRAINED OPTIMIZATION

A trust-region algorithm is presented for a nonlinear optimization problem of equality-constraints. The characterization of the algorithm is using inexact gradient information. Global convergence results are demonstrated where the gradient values are obeyed a simple relative error condition.

An iterative algorithm of NWTLS-EC for three dimensional-datum transformation with large rotation angle

The Gauss-Markov （GM） model and the Errors-in-Variables （EIV） model are frequently used to perform 3D coordinate transformations in geodesy and engineering surveys. In these applications, because the observation errors in original coordinates system are also taken into account, the latter is more accurate and reasonable than the former. Although the Weighted Total Least Squares （WTLS） technique has been intro- duced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance- Covariance Matrix （VCM） of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account. Because the 3D datum transformation with large rotation angle is a non- linear problem, the WTLS is no longer suitable in this ease. In this contribution, we suggested the nonlinear WTLS adjustments with equality constraints （NWTLS-EC） for 3D datum transformation with large rotation an- gle, which removed the particular structure restriction on the VCM. The Least Squares adjustment with Equality （LSE） constraints is employed to solve NWTLS-EC as the nonlinear model has been linearized, and an iterative algorithm is proposed with the LSE solution. A simulation study of 3D datum transformation with large rotation angle is given to insight into the feasibility of our algorithm at last.

Method for solving fully fuzzy linear programming problems using deviation degree measure

A new fully fuzzy linear programming （FFLP） problem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crisp 6-parametric linear programming （LP） problem. Giving the value of deviation degree in each constraint, the 6-fuzzy optimal solution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict： to improve the values of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to illustrate the proposed method.

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.

A New Method of Moving Asymptotes for Large-scale Linearly Equality-constrained Minimization

A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed. In this method, linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved. The numerical results show that the new method may be capable of processing some large scale problems.

Equality-constrained minimization of polynomial functions

This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.

A GLOBALLY CONVERGENT TRUST REGION ALGORITHM FOR OPTIMIZATION WITH GENERAL CONSTRAINTS AND SIMPLE BOUNDS

In this paper, we introduce a concept of substationary points and present a new trust region-based method for the optimization problems with general nonlinear equality constraints and simple bounds. Without the linear independent assumption on the gradients of the equalitiy constraints, we prove the global convergence results for the main algorithm and indicate that they extend the results on SQP and those on trust region methods for equality constrained optimizstion and for optimization with simple bounds. Moreover, since any nonlinear programming problem can be converted into the standard nonlinear programming by introducing slack variables, the trust region method preseated in this paper can be used for solving general nonlinear programming problems.

Parametric Duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions

A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.

Global Parametric Sufficient Optimality Conditions for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-invex Functions

In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.

A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

Parametric Duality Models for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized (α, η, ρ)-V-Invex Functions

In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.

Global Parametric Sufficient Efficiency Conditions for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized (α, η, ρ)-V-Invex Functions

Abstract In this paper, we discuss numerous sets of global parametric sufficient efficiency conditions under various generalized （a,n, p）-V-invexity assumptions for a semiinfinite multiobjective fractional programming problem.