Studying the theoretical properties of optimization algorithms such as genetic and evolutionary strategies allows us to determine when they are suitable for solving a particular type problem. Such study consists three main steps. The first step is considering Stochastic Global Optimization Algorithms (SGoals ), i.e., iterative algorithm that applies stochastic operations set candidate solutions...

We propose a stochastic optimization model for the Multiperiod Multiproduct Advertising Budgeting problem, so that the expected profit of the advertising investment is maximized. The model is a convex optimization problem that can readily be solved by plain use of standard optimization software. It has been tested for planning a realistic advertising campaign. In our case study, the expected pr...

We present a reformulation of stochastic global optimization as a filtering problem. The motivation behind this reformulation comes from the fact that for many optimization problems we cannot evaluate exactly the objective function to be optimized. Similarly, we may not be able to evaluate exactly the functions involved in iterative optimization algorithms. For example, we may only have access ...

Zero-sum stochastic games are easy to solve as they can be cast as simple Markov decision processes. This is however not the case with general-sum stochastic games. A fairly general optimization problem formulation is available for general-sum stochastic games by Filar and Vrieze [2004]. However, the optimization problem there has a non-linear objective and non-linear constraints with special s...

The stochastic composition optimization proposed recently by Wang et al. [2014] minimizes the objective with the compositional expectation form: minx (EiFi ◦ EjGj)(x). It summarizes many important applications in machine learning, statistics, and finance. In this paper, we consider the finite-sum scenario for composition optimization: min x f (x) := 1 n n ∑ i=1 Fi ( 1 m m ∑ j=1 Gj(x) ) . We pro...

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method...

Optimization of expected values in a stochastic domain is common in real world applications. However, it is often difficult to solve such optimization problems without significant knowledge about the surface defined by the stochastic function. I n this paper we examine local search techniques to solve stochastic Optimization. I n particular, we analyze assumptions of smoothness upon which these...

We propose a stochastic variance-reduced cubic regularized Newton method for non-convex optimization. At the core of our algorithm is a novel semi-stochastic gradient along with a semi-stochastic Hessian, which are specifically designed for cubic regularization method. We show that our algorithm is guaranteed to converge to an ( , √ )-approximately local minimum within Õ(n/ ) second-order oracl...

due to the probabilistic nature and uncertainties of structural parameters, reliability-based optimization will enable engineers to account for the safety of the structures and allow for its decision making applicability. thus, reliability-based design will substitute deterministic rules of codes of practice. space structures are of those types that have an exceedingly high range of applicabili...