共查询到19条相似文献,搜索用时 156 毫秒
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借助于强次可行方向法的思想和滤子法的思想,给出了一种求解非线性约束优化问题的无罚函数无滤子的方法.方法借助于广义投影技术产生搜索方向,直接通过原目标函数和约束违反度函数作为搜索函数来产生步长,有效地避免了消耗计算成本的恢复阶段.最后在适当的假设条件下,给出了算法的全局收敛性和有效性. 相似文献
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本文利用广义投影技术和滤子技术相结合的方法来求解非线性规划问题,该方法只需要通过求解一个子问题获得主搜索方向或计算一次广义投影型辅助方向,避免了常规滤子法中的恢复算法,而且能有效避免选择罚函数的困难,大大简化了计算量.同时,在不需要严格互补的条件下获得了算法的全局收敛性. 相似文献
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设计了求解不等式约束非线性规划问题的一种新的滤子序列线性方程组算法,该算法每步迭代由减小约束违反度和目标函数值两部分构成.利用约束函数在某个中介点线性化的方法产生搜索方向.每步迭代仅需求解两个线性方程组,计算量较小.在一般条件下,证明了算法产生的无穷迭代点列所有聚点都是可行点并且所有聚点都是所求解问题的KKT点. 相似文献
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设计了一个新的求解等式约束优化问题的非单调信赖域算法.该算法不需要罚函数也无需滤子.在每次迭代过程中只需求解满足下降条件的拟法向步及切向步.新算法产生的迭代步比滤子方法更易接受,计算量比单调算法小.在一般条件下,算法具有全局收敛性. 相似文献
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《数学物理学报(A辑)》2020,(3)
该文考虑求解带非线性不等式和等式约束的极大极小优化问题,借助半罚函数思想,提出了一个新的广义投影算法.该算法具有以下特点:由一个广义梯度投影显式公式产生的搜索方向是可行下降的;构造了一个新型的最优识别控制函数;在适当的假设条件下具有全局收敛性和强收敛性.最后,通过初步的数值试验验证了算法的有效性. 相似文献
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结合罚函数思想和广义梯度投影技术,提出求解非线性互补约束数学规划问题的一个广义梯度投影罚算法.首先,通过扰动技术和广义互补函数,将原问题转化为序列带参数的近似的标准非线性规划;其次,利用广义梯度投影矩阵构造搜索方向的显式表达式.一个特殊的罚函数作为效益函数,而且搜索方向能保证效益函数的下降性.在适当的假设条件下算法具有全局收敛性. 相似文献
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在本文中,我们提出了一种新的带扰动项的三项记忆梯度混合投影算法.在这种方法中应用了广义Armijo线搜索,并且仅在梯度函数在包含迭代序列的开凸集上一致连续的条件下证明了该算法的全局收敛性.最后给出了几个数值算例. 相似文献
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提出了一个任意初始点的广义梯度滤子方法. 该方法不使用罚函数以避免由此带来的缺陷并可以减少计算量. 方法的另一个特点是不因使用了滤子技术而使算法早熟或陷入循环. 算法对初始点没有要求并在比较合理的条件下具有全局收敛性. 相似文献
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In this article, an affine scaling interior trust-region algorithm which employs backtracking line search with filter technique is presented for solving nonlinear equality constrained programming with nonnegative constraints on variables. At current iteration, the general full affine scaling trust-region subproblem is decomposed into a pair of trust-region subproblems in vertical and horizontal subspaces, respectively. The trial step is given by the solutions of the pair of trust-region subproblems. Then, the step size is decided by backtracking line search together with filter technique. This is different from traditional trust-region methods and has the advantage of decreasing the number of times that a trust-region subproblem must be resolved in order to determine a new iteration point. Meanwhile, using filter technique instead of merit function to determine a new iteration point can avoid the difficult decisions regarding the choice of penalty parameters. Under some reasonable assumptions, the new method possesses the property of global convergence to the first-order critical point. Preliminary numerical results show the effectiveness of the proposed algorithm. 相似文献
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《Optimization》2012,61(2):137-150
An algorithm for addressing multiple objective linear programming (MOLP) problems is presented. The algorithm modifies the path-following primal-dual algorithm to MOLP problems by using the single objective algorithm to generate interior search directions and later combine them to derive a single direction along which to step to the next iterate. Combining the different interior search directions is done by interacting with a Decision Maker (DM) to obtain locally-relevant preference information for the value vectors along these directions. This preference information is then used to derive an approximation to the gradient of an implicity-known utility function, and using a projection of this gradient provides a direction gradient of an implicitly-known utility function, and using a projection of this gradient provides a direction vector along which we step to the next iterate. At each iteration the algorithm also generates boundary points that aid in deriving the combined search direction. We refer to these boundary points, generated sequentially during the process, as anchor points that serve as candidate solutions at which to terminate the iterative process. 相似文献
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给求解无约束规划问题的记忆梯度算法中的参数一个特殊取法,得到目标函数的记忆梯度G o ldste in-L av in tin-Po lyak投影下降方向,从而对凸约束的非线性规划问题构造了一个记忆梯度G o ldste in-L av in tin-Po lyak投影算法,并在一维精确步长搜索和去掉迭代点列有界的条件下,分析了算法的全局收敛性,得到了一些较为深刻的收敛性结果.同时给出了结合FR,PR,HS共轭梯度算法的记忆梯度G o ldste in-L av in tin-Po lyak投影算法,从而将经典共轭梯度算法推广用于求解凸约束的非线性规划问题.数值例子表明新算法比梯度投影算法有效. 相似文献
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《Applied Mathematics Letters》2007,20(4):405-411
In this work, combining the generalized projection techniques with the idea of a strongly sub-feasible direction method, a new algorithm for solving systems of nonlinear inequalities is presented. At each iteration of the proposed algorithm, the search direction is yielded by just one new explicit formula. The proposed algorithm is proved not only to possess global and strong convergence but also to be able to produce a solution in a finite number of iterations. Finally, some interesting numerical results are reported. 相似文献