2 research outputs found
Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems
The paper deals with stochastic difference-of-convex functions (DC) programs,
that is, optimization problems whose the cost function is a sum of a lower
semicontinuous DC function and the expectation of a stochastic DC function with
respect to a probability distribution. This class of nonsmooth and nonconvex
stochastic optimization problems plays a central role in many practical
applications. Although there are many contributions in the context of convex
and/or smooth stochastic optimization, algorithms dealing with nonconvex and
nonsmooth programs remain rare. In deterministic optimization literature, the
DC Algorithm (DCA) is recognized to be one of the few algorithms to solve
effectively nonconvex and nonsmooth optimization problems. The main purpose of
this paper is to present some new stochastic DCAs for solving stochastic DC
programs. The convergence analysis of the proposed algorithms is carefully
studied, and numerical experiments are conducted to justify the algorithms'
behaviors
Solving Nonsmooth Nonconvex Compound Stochastic Programs with Applications to Risk Measure Minimization
This paper studies a structured compound stochastic program (SP) involving
multiple expectations coupled by nonconvex and nonsmooth functions. We present
a successive convex-programming based sampling algorithm and establish its
subsequential convergence. We describe stationarity properties of the limit
points for several classes of the compound SP. We further discuss probabilistic
stopping rules based on the computable error-bound for the algorithm. We
present several risk measure minimization problems that can be formulated as
such a compound stochastic program; these include generalized deviation
optimization problems based on optimized certainty equivalent and buffered
probability of exceedance (bPOE), a distributionally robust bPOE optimization
problem, and a multiclass classification problem employing the cost-sensitive
error criteria with bPOE risk measure