In this paper, we consider expected value, variance and worst-case optimization of nonlinear models. We present algorithms for computing optimal expected values, and variance, based on iterative Taylor expansions. We establish convergence and consider the relative merits of policies beaded on...

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand...

Analyses of global climate policy as a sequential decision under uncertainty have been severely restricted by dimensionality and computational burdens. Therefore, they have limited the number of decision stages, discrete actions, or number and type of uncertainties considered. In particular, two...

In this paper, we consider expected value, variance and worst-case optimization of nonlinear models. We present algorithms for computing optimal expected values, and variance, based on iterative Taylor expansions. We establish convergence and consider the relative merits of policies beaded on...

In this paper, we consider expected value, variance and worst-case optimization of nonlinear models. We present algorithms for computing optimal expected values, and variance, based on iterative Taylor expansions. We establish convergence and consider the relative merits of policies beaded on...

We consider the problem of finding the minimum of a real-valued multivariate polynomial function constrained in a compact set defined by polynomial inequalities and equalities. This problem, called polynomial optimization problem (POP), is generally nonconvex and has been of growing interest to...

We consider polynomial optimization problems pervaded by a sparsity pattern. It has been shown in [1, 2] that the optimal solution of a polynomial programming problem with structured sparsity can be computed by solving a series of semidefinite relaxations that possess the same kind of sparsity....