CAJ | 학술논문

提供了一种新的非单调内点回代线搜索技术的仿射内点信赖域方法解线性不等式约束的广义非线性互补问题(GCP).基于广义互补问题构成的半光滑方程组的广义Jacobian矩阵,算法使用l2范数作为半光滑方程组的势函数,形成的信赖域子问题为一个带椭球约束的线性化的二次模型.利用广义牛顿方程计算试探迭代步,通过内点映射回代技术确保迭代点是严格内点,保证了算法的整体收敛性.在合理的条件下,证明了信赖域算法在接近最优点时可转化为广义拟牛顿步,进而具有局部超线性收敛速率.非单调技术将克服高度非线性情况加速收敛进展.最后,数值结果表明了算法的有效性.
제공료일충신적비단조내점회대선수색기술적방사내점신뢰역방법해선성불등식약속적엄의비선성호보문제(GCP).기우엄의호보문제구성적반광활방정조적엄의Jacobian구진,산법사용l2범수작위반광활방정조적세함수,형성적신뢰역자문제위일개대타구약속적선성화적이차모형.이용엄의우돈방정계산시탐질대보,통과내점영사회대기술학보질대점시엄격내점,보증료산법적정체수렴성.재합리적조건하,증명료신뢰역산법재접근최우점시가전화위엄의의우돈보,진이구유국부초선성수렴속솔.비단조기술장극복고도비선성정황가속수렴진전.최후,수치결과표명료산법적유효성.
This paper proposes a new affine scaling trust-region method in association with nonmonotonic interior backtracking line search technique for solving the generalized complementarity problems (GCP) with linear inequality constraints.The proposed algorithm uses a generalized Jacobian of the function involved the semismooth equations reformulated from the GCP and adopts squared Euclidean norm of the semismooth equations as a merit function.Based on a simply constrained differentiable minimization reformulation,the trustregion subproblem is defined by minimizing the local quadratic approximation of the squared Euclidean norm of the semismooth systems adding the augmented quadratic affine scaling term subject only to an ellipsoidal constraint.The global convergence results are developed in a very general setting of computing trial steps by a generalized Newton-like method while the strict interior feasibility is augmented by an interior projective backtracking technique.The authors establish that close to a regular solution the trust-region algorithm turns into the generalized Newton method under some mild conditions,which is shown to converge locally q-superlinearly.A nonmonotonic backtracking criterion should bring about speeding up the convergence progress under some large curvature curves of the contours of merit function.The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.