7 The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the Unit Commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that restrict their application to real-world systems. This paper demon...

An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established. For a nondegenerate stationary point, the algorithm eventually reduces to unconstrained optimization with...

In this paper, we propose formulations and algorithms for robust portfolio optimization under both aleatory uncertainty (i.e., natural variability) and epistemic uncertainty (i.e., imprecise probabilistic information) arising from interval data. Epistemic uncertainty is represented using two approaches: (1) moment bounding approach and (2) likelihood-based approach. This paper first proposes a ...

Given a compact basic semi-algebraic set K ⊂ Rn×Rm, a simple set B (box or ellipsoid), and some semi-algebraic function f , we consider sets defined with quantifiers, of the form Rf := {x ∈ B : f(x,y) ≤ 0 for all y such that (x,y) ∈ K} Df := {x ∈ B : f(x,y) ≤ 0 for some y such that (x,y) ∈ K}. The former set Rf is particularly useful to qualify “robust” decisions x versus noise parameter y (e.g...

We introduce an unconstrained multicriteria optimization problem and discuss its relation to various well-known scalar robust optimization problems with a finite uncertainty set. Specifically, we show that a unique solution of a robust optimization problem is Pareto optimal for the unconstrained optimization problem. Furthermore, it is demonstrated that the set of weakly Pareto optimal solution...

Abstract Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, the application those strategies is exported to Riemannian optimization, wherein minimization be performed with respect variables restricted lie on manifold. More specifically, classic linesearch extrapolated variants direct are considered, tailored devi...

The purpose of this research is predicting the stock prices using the Particle Swarm Optimization Algorithm and Box-Jenkins method. In this way, the information of 165 corporations is collected from 2001 to 2016. Then, this research considers price to earnings per share and earnings per share as main variables. The relevant regression equation was created using two variables of earnings per sha...

Optimization of very expensive black-box functions requires utilization of maximum information gathered by the process of optimization. Model Guided Sampling Optimization (MGSO) forms a more robust alternative to Jones’ Gaussian-process-based EGO algorithm. Instead of EGO’s maximizing expected improvement, the MGSO uses sampling the probability of improvement which is shown to be helpful agains...