Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new ...Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.展开更多
针对只有硬模块的布图规划问题,通常将其构建成组合优化模型,但求解过程时间成本高。为提高求解效率,提出了一种基于非光滑解析数学规划的布图规划算法。基于布图中器件的坐标表示,构建了一个泛化的非光滑解析数学规划模型,将不同场景...针对只有硬模块的布图规划问题,通常将其构建成组合优化模型,但求解过程时间成本高。为提高求解效率,提出了一种基于非光滑解析数学规划的布图规划算法。基于布图中器件的坐标表示,构建了一个泛化的非光滑解析数学规划模型,将不同场景下的布图规划问题的不同优化阶段处理为该泛化模型的特例,并利用共轭次梯度算法(conjugate sub-gradient algorithm,CSA)对其进行求解。针对固定轮廓布图规划问题,通过统一框架下的全局布图规划、合法化、局部优化三个阶段,实现了在固定轮廓约束下的线长优化。针对无固定轮廓约束问题,提出了带黄金分割策略的共轭次梯度算法(conjugate sub-gradient algorithm with golden section strategy,CSA_GSS),利用黄金分割策略缩小固定轮廓的面积,达到面积和线长双优化的效果。实验在GSRC测试电路上与基于B*-树表示的布图规划算法进行比较,该算法对于大规模电路在线长和时间方面均占据优势。实验结果表明,该算法能以更低的时间复杂度获得更优的线长。展开更多
Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stocha...Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.展开更多
基金supported by the Key Foundation of Southwest University for Nationalities(09NZD001).
文摘Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.
文摘针对只有硬模块的布图规划问题,通常将其构建成组合优化模型,但求解过程时间成本高。为提高求解效率,提出了一种基于非光滑解析数学规划的布图规划算法。基于布图中器件的坐标表示,构建了一个泛化的非光滑解析数学规划模型,将不同场景下的布图规划问题的不同优化阶段处理为该泛化模型的特例,并利用共轭次梯度算法(conjugate sub-gradient algorithm,CSA)对其进行求解。针对固定轮廓布图规划问题,通过统一框架下的全局布图规划、合法化、局部优化三个阶段,实现了在固定轮廓约束下的线长优化。针对无固定轮廓约束问题,提出了带黄金分割策略的共轭次梯度算法(conjugate sub-gradient algorithm with golden section strategy,CSA_GSS),利用黄金分割策略缩小固定轮廓的面积,达到面积和线长双优化的效果。实验在GSRC测试电路上与基于B*-树表示的布图规划算法进行比较,该算法对于大规模电路在线长和时间方面均占据优势。实验结果表明,该算法能以更低的时间复杂度获得更优的线长。
文摘Proximal gradient descent and its accelerated version are resultful methods for solving the sum of smooth and non-smooth problems. When the smooth function can be represented as a sum of multiple functions, the stochastic proximal gradient method performs well. However, research on its accelerated version remains unclear. This paper proposes a proximal stochastic accelerated gradient (PSAG) method to address problems involving a combination of smooth and non-smooth components, where the smooth part corresponds to the average of multiple block sums. Simultaneously, most of convergence analyses hold in expectation. To this end, under some mind conditions, we present an almost sure convergence of unbiased gradient estimation in the non-smooth setting. Moreover, we establish that the minimum of the squared gradient mapping norm arbitrarily converges to zero with probability one.
