本文通过连续可微的非凸函数所形成的概率约束,来分析概率约束问题。描述了潜在的概率函数的水平集的切锥和法锥。进一步,基于p-有效点的概念,形成这些问题的一阶和二阶最优性条件。对于离散分布函数的这种情况,产生一个基于修正的指数...本文通过连续可微的非凸函数所形成的概率约束,来分析概率约束问题。描述了潜在的概率函数的水平集的切锥和法锥。进一步,基于p-有效点的概念,形成这些问题的一阶和二阶最优性条件。对于离散分布函数的这种情况,产生一个基于修正的指数函数的对偶算法来解决概率约束问题。In this paper, the problem of probability constraints is analyzed by means of the probability constraints formed by continuously differentiable non-convex functions. The tangent and normal cones of the level set of potential probability functions are described. Further, based on the concept of p-efficient points, the first and second order optimality conditions of these problems are formed. For this case of the discrete distribution function, a dual algorithm based on the modified exponential function is generated to solve the probability constraint problem.展开更多
文摘本文通过连续可微的非凸函数所形成的概率约束,来分析概率约束问题。描述了潜在的概率函数的水平集的切锥和法锥。进一步,基于p-有效点的概念,形成这些问题的一阶和二阶最优性条件。对于离散分布函数的这种情况,产生一个基于修正的指数函数的对偶算法来解决概率约束问题。In this paper, the problem of probability constraints is analyzed by means of the probability constraints formed by continuously differentiable non-convex functions. The tangent and normal cones of the level set of potential probability functions are described. Further, based on the concept of p-efficient points, the first and second order optimality conditions of these problems are formed. For this case of the discrete distribution function, a dual algorithm based on the modified exponential function is generated to solve the probability constraint problem.