Related papers: Two-Stage Robust Quadratic Optimization with Equal…
In this paper, we study the two-stage distributionally robust optimization (DRO) problem from the primal perspective. Unlike existing approaches, this perspective allows us to build a deeper and more intuitive understanding on DRO, to…
In the realm of robust optimization the k-adaptability approach is one promising method to derive approximate solutions for two-stage robust optimization problems. Instead of allowing all possible second-stage decisions, the k-adaptability…
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time…
In this paper a class of combinatorial optimization problems is discussed. It is assumed that a feasible solution can be constructed in two stages. In the first stage the objective function costs are known while in the second stage they are…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
Many practical optimization problems involve uncertain parameters that are strictly positive. However, the most common uncertainty sets used in robust optimization are the box and the ellipsoidal sets, which may include non-positive values…
In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…
In this paper, we study a fixed-confidence, fixed-tolerance formulation of a class of stochastic bi-level optimization problems, where the upper-level problem selects from a finite set of systems based on a performance metric, and the…
Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems and are not applicable for complex systems consisting of multiple components, due…
There is a growing need for new optimization methods to facilitate the reliable and cost-effective operation of power systems with intermittent renewable energy resources. In this paper, we formulate the robust AC optimal power flow…
In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line search…
Multi-stage decision-making under uncertainty, where decisions are taken under sequentially revealing uncertain problem parameters, is often essential to faithfully model managerial problems. Given the significant computational challenges…
We propose a two-stage penalized least squares method to build large systems of structural equations based on the instrumental variables view of the classical two-stage least squares method. We show that, with large numbers of endogenous…
Randomness is ubiquitous in modern engineering. The uncertainty is often modeled as random coefficients in the differential equations that describe the underlying physics. In this work, we describe a two-step framework for numerically…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which…
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…
We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the…
We study piecewise affine policies for multi-stage adjustable robust optimization (ARO) problems with non-negative right-hand side uncertainty. First, we construct new dominating uncertainty sets and show how a multi-stage ARO problem can…
This paper considers the linear-quadratic dual control problem where the system parameters need to be identified and the control objective needs to be optimized in the meantime. Contrary to existing works on data-driven linear-quadratic…