求解Minimax优化问题的SQP方法

本文提出一类求解minimax优化问题的有效算法,该算法属于序列二次规划方法.它具有全局收敛性和超线性收敛速率.数值例子表明,该算法是非常有效的,这与算法具有良好的理论结果是分不开的.     

MBFGS修正在SQP算法中的应用—算法及其局部收敛性

本研究了SQP算法中保持矩阵正定性的方法．利用Li—Fukmshima提出的求解无约束问题的修正BFGS(MBFGS)公式，提出了求解等式约束问题的SQP算法．证明了若在问题的解处二阶充分条件成立，则相应的SQP算法具有2一一步超线性收敛性．     

General Information

In this paper, a new sequential penalty algorithm, based on the L_infin exact penalty function, is proposed for a general nonlinear constrained optimization problem. The algorithm has the following characteristics: it can start from an arbitrary initial point; the feasibility of the subproblem is guaranteed; the penalty parameter is adjusted automatically; global convergence without any regularity assumption is proved. The update formula of the penalty parameter is new. It is proved that the algorithm proposed in this paper behaves equivalently to the standard SQP method after sufficiently many iterations. Hence, the local convergence results of the standard SQP method can be applied to this algorithm. Preliminary numerical experiments show the efficiency and stability of the algorithm.     

A new technique for inconsistent QP problems in the SQP method

Successful treatment of inconsistent QP problems is of major importance in the SQP method, since such occur quite often even for well behaved nonlinear programming problems. This paper presents a new technique for regularizing inconsistent QP problems, which compromises in its properties between the simple technique of Pantoja and Mayne [36] and the highly successful, but expensive one of Tone [47]. Global convergence of a corresponding algorithm is shown under reasonable weak conditions. Numerical results are reported which show that this technique, combined with a special method for the case of regular subproblems, is quite competitive to highly appreciated established ones.     

An SQP algorithm with cautious updating criteria for nonlinear degenerate problems

An efficient SQP algorithm for solving nonlinear degenerate problems is proposed in the paper. At each iteration of the algorithm, a quadratic programming subproblem, which is always feasible by introducing a slack variable, is solved to obtain a search direction. The steplength along this direction is computed by employing the 1∞ exact penalty function through Armijo-type line search scheme. The algorithm is proved to be convergent globally under mild conditions.     

A Globally and Superlinearly Convergent SQP Algorithm for Nonlinear Constrained Optimization

Based on a continuously differentiable exact penalty function and a regularization technique for dealing with the inconsistency of subproblems in the SQP method, we present a new SQP algorithm for nonlinear constrained optimization problems. The proposed algorithm incorporates automatic adjustment rules for the choice of the parameters and makes use of an approximate directional derivative of the merit function to avoid the need to evaluate second order derivatives of the problem functions. Under mild assumptions the algorithm is proved to be globally convergent, and in particular the superlinear convergence rate is established without assuming that the strict complementarity condition at the solution holds. Numerical results reported show that the proposed algorithm is promising.     

An SQP-type algorithm for nonlinear second-order cone programs

We propose an SQP-type algorithm for solving nonlinear second-order cone programming (NSOCP) problems. At every iteration, the algorithm solves a convex SOCP subproblem in which the constraints involve linear approximations of the constraint functions in the original problem and the objective function is a convex quadratic function. Those subproblems can be transformed into linear SOCP problems, for which efficient interior point solvers are available. We establish global convergence and local quadratic convergence of the algorithm under appropriate assumptions. We report numerical results to examine the effectiveness of the algorithm. This work was supported in part by the Scientific Research Grant-in-Aid from Japan Society for the Promotion of Science.     

求解一般约束优化问题的一个全局收敛的混合不精确SQP算法

对于一般约束优化问题,本文通过一种特殊的耦合策略,把一个局邵超线性收敛的不精确SQP算法与广义梯度投影法相结合,从而给出了一个混合算法.该算法无需计算拉格朗日函数的海色矩阵,并且在适当的假设下,算法具有全局和局部超线性收敛性.     

A SQP METHOD FOR MINIMIZING A CLASS OF NONSMOOTH FUNCTIONS

In this paper,we present a successive quadratic programming(SQP)method for minimizing a class of nonsmooth functions,which are the sum of a convex function and a nonsmooth composite function.The method generates new iterations by using the Armijo-type line search technique after having found the search directions.Global convergence property is established under mild assumptions.Numerical results are also offered.     

A New Trust-Region Algorithm for Equality Constrained Optimization

We present a new trust-region algorithm for solving nonlinear equality constrained optimization problems. Quadratic penalty functions are employed to obtain global convergence. At each iteration a local change of variables is performed to improve the ability of the algorithm to follow the constraint level set. Under certain assumptions we prove that this algorithm globally converges to a point satisfying the second-order necessary optimality conditions. Results of preliminary numerical experiments are reported.