An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each ite...An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.展开更多
由日前和实时市场组成的2市场交易机制是目前普遍存在的电力市场交易机制,在2市场中发电商的电量分配和竞价决策以及风险评估等都是受到广泛关注的问题。指出了现有文献在借鉴经济学和金融学的理论模型来研究多交易市场中发电商竞价策...由日前和实时市场组成的2市场交易机制是目前普遍存在的电力市场交易机制,在2市场中发电商的电量分配和竞价决策以及风险评估等都是受到广泛关注的问题。指出了现有文献在借鉴经济学和金融学的理论模型来研究多交易市场中发电商竞价策略时存在的问题。首先在分析了发电商竞价结果的概率分布之后,提出了发电商竞价成功概率分布函数的概念。然后基于日前和实时市场中投标结构的特点,针对采用分段报价和按报价结算(pay as bid price,PAB)方式的电力市场,建立了日前和实时市场中发电商的多目标二层规划竞价策略模型,并设计了以蒙特卡罗方法和遗传算法为基础的求解算法。最后采用算例对所提出的模型和算法进行了仿真验证。展开更多
文摘An augmented Lagrangian trust region method with a bi=object strategy is proposed for solving nonlinear equality constrained optimization, which falls in between penalty-type methods and penalty-free ones. At each iteration, a trial step is computed by minimizing a quadratic approximation model to the augmented Lagrangian function within a trust region. The model is a standard trust region subproblem for unconstrained optimization and hence can efficiently be solved by many existing methods. To choose the penalty parameter, an auxiliary trust region subproblem is introduced related to the constraint violation. It turns out that the penalty parameter need not be monotonically increasing and will not tend to infinity. A bi-object strategy, which is related to the objective function and the measure of constraint violation, is utilized to decide whether the trial step will be accepted or not. Global convergence of the method is established under mild assumptions. Numerical experiments are made, which illustrate the efficiency of the algorithm on various difficult situations.
文摘由日前和实时市场组成的2市场交易机制是目前普遍存在的电力市场交易机制,在2市场中发电商的电量分配和竞价决策以及风险评估等都是受到广泛关注的问题。指出了现有文献在借鉴经济学和金融学的理论模型来研究多交易市场中发电商竞价策略时存在的问题。首先在分析了发电商竞价结果的概率分布之后,提出了发电商竞价成功概率分布函数的概念。然后基于日前和实时市场中投标结构的特点,针对采用分段报价和按报价结算(pay as bid price,PAB)方式的电力市场,建立了日前和实时市场中发电商的多目标二层规划竞价策略模型,并设计了以蒙特卡罗方法和遗传算法为基础的求解算法。最后采用算例对所提出的模型和算法进行了仿真验证。
