论文标题
0/1限制优化解决样本的平均近似值，以限制限制的编程
0/1 Constrained Optimization Solving Sample Average Approximation for Chance Constrained Programming
论文作者
论文摘要
样本平均近似值（SAA）是处理机会受限的编程，这是一个具有挑战性的随机优化问题。 SAA的约束的特征是$ 0/1 $损失函数，在设计数值算法时会导致相当复杂。大多数现有方法都是根据SAA的重新制定的，例如二进制整数编程或轻松的问题。但是，直接解决SAA的可行方法的发展仍然难以捉摸，更不用说提供理论保证了。在本文中，我们调查了一般$ 0/1 $限制优化的优化，提供了一种解决SAA而不是其重新制定的新方法。具体而言，从推导Bouligand Tangent和Fr $ \ acute {e} $ CHET普通锥开始，我们建立了几个最佳条件。其中一个可以通过方程系统等效地表达，从而使牛顿型算法的开发能够开发。该算法在标准假设下展示了本地超级线性或二次收敛速率，与几个领先的求解器相比，数值性能很好。
Sample average approximation (SAA) is a tractable approach for dealing with chance constrained programming, a challenging stochastic optimization problem. The constraint of SAA is characterized by the $0/1$ loss function which results in considerable complexities in devising numerical algorithms. Most existing methods have been devised based on reformulations of SAA, such as binary integer programming or relaxed problems. However, the development of viable methods to directly tackle SAA remains elusive, let alone providing theoretical guarantees. In this paper, we investigate a general $0/1$ constrained optimization, providing a new way to address SAA rather than its reformulations. Specifically, starting with deriving the Bouligand tangent and Fr$\acute{e}$chet normal cones of the $0/1$ constraint, we establish several optimality conditions. One of them can be equivalently expressed by a system of equations, enabling the development of a semismooth Newton-type algorithm. The algorithm demonstrates a locally superlinear or quadratic convergence rate under standard assumptions, along with nice numerical performance compared to several leading solvers.
