Convergence analysis of a nonlinear Lagrange algorithm for general nonlinear constrained optimization problems

The convergence analysis of a nonlinear Lagrange algorithm for solving nonlinear constrained optimization problems with both inequality and equality constraints is explored in detail. The estimates for the derivatives of the multiplier mapping and the solution mapping of the proposed algorithm are discussed via the technique of the singular value decomposition of matrix. Based on the estimates, the local convergence results and the rate of convergence of the algorithm are presented when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions. Furthermore, the condition number of the Hessian of the nonlinear Lagrange function with respect to the decision variables is analyzed, which is closely related to efficiency of the algorithm. Finally, the preliminary numericM results for several typical test problems are reported.

AN SQP ALGORITHM WITH NONMONOTONE LINE SEARCHFOR GENERAL NONLINEAR CONSTRAINED OPTIMIZATION PROBLEM

In this paper, an SQP type algorithm with a new nonmonotone line search technique for general constrained optimization problems is presented. The new algorithm does not have to solve the second order correction subproblems for each iterations, but still can circumvent the so-called Maratos effect. The algorithm's global convergence and superlinear convergent rate have been proved. In addition, we can prove that, after a few iterations, correction subproblems need not be solved, so computation amount of the algorithm will be decreased much more. Numerical experiments show that the new algorithm is effective.

Improved algorithms to plan missions for agile earth observation satellites

This study concentrates of the new generation of the agile （AEOS）. AEOS is a key study object on management problems earth observation satellite in many countries because of its many advantages over non-agile satellites. Hence, the mission planning and scheduling of AEOS is a popular research problem. This research investigates AEOS characteristics and establishes a mission planning model based on the working principle and constraints of AEOS as per analysis. To solve the scheduling issue of AEOS, several improved algorithms are developed. Simulation results suggest that these algorithms are effective.

深水支持平台火灾定量风险评估

The living area of an offshore platform is the main living place for operators in offshore oil and gas fields.Fire risk assessment plays an important role in the safety of personnel in offshore platforms.In this paper,a fire risk assessment mathematical model for offshore platfoms is proposed based on a comprehensive safety assessment method.The concept of danger time is presented according to the evaluation criteria of safe evacuation.The fire risk of offshore platforms is assessed by combining probability statistics with numerical simulation.The fire risk is quantitatively assessed by using an N500 deep water semi-submersible support platform as an example.According to the FN curve,fire frequency,fire escalation probability,and casualty probability,the rationality of marine general layout is analyzed,and the general layout design could be optimized to reduce the fire risk.

RECOVERY A POSTERIORI ERROR ESTIMATES FOR GENERAL CONVEX ELLIPTIC OPTIMAL CONTROL PROBLEMS SUBJECT TO POINTWISE CONTROL CONSTRAINTS

Superconvergence and recovery a posteriori error estimates of the finite element ap- proximation for general convex optimal control problems are investigated in this paper. We obtain the superconvergence properties of finite element solutions, and by using the superconvergence results we get recovery a posteriori error estimates which are asymptotically exact under some regularity conditions. Some numerical examples are provided to verify the theoretical results.

Recovery Type A Posteriori Error Estimates of Fully Discrete Finite Element Methods for General Convex Parabolic Optimal Control Problems

This paper is concerned with recovery type a posteriori error estimates of fully discrete finite element approximation for general convex parabolic optimal control problems with pointwise control constraints.The time discretization is based on the backward Euler method.The state and the adjoint state are approximated by piecewise linear functions and the control is approximated by piecewise constant functions.We derive the superconvergence properties of finite element solutions.By using the superconvergence results,we obtain recovery type a posteriori error estimates.Some numerical examples are presented to verify the theoretical results.

General Admissibility for Linear Estimators in a General Multivariate Linear Model under Balanced Loss Function

A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.

ON THE OPTIMALITY IN GENERAL SENSE FOR ODD-BLOCK SEARCH

In his classical article[3], J. Kiefer introduced the Fibonacci search as a direct optimal method. The optimality was proved under the restriction: the total number of tests is given in advance and fixed. To avoid this restriction, some different concepts of optimality were proposed and some corresponding optimal methods were obtained in [1], [2], [5] and [6]. In particular, the even-block search was treated in [1]. This paper deals with the odd-block search. The main result is Theorem 1.15.