A large number of practical algorithms for Optimal Control Problems (OCP) relies on a so-called condensing procedure to exploit the given structure in the quadratic programming (QP) subproblems. While the established structure-exploiting condensing algorithm is of cubic complexity in the horizon length, in this technical note we propose a novel algorithm that is only of … Read more
In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to … Read more
We consider the context of “simulation-based recursions,” that is, recursions that involve quantities needing to be estimated using a stochastic simulation. Examples include stochastic adaptations of fixed-point and gradient descent recursions obtained by replacing function and derivative values appearing within the recursion by their Monte Carlo counterparts. The primary motivating settings are Simulation Optimization and … Read more
We describe a simulation-based optimization method that allocates additional capacity to transmission lines in order to minimize the expected value of the load shed due to a cascading blackout. Estimation of the load-shed distribution is accomplished via the ORNL-PSerc-Alaska (OPA) simulation model, which solves a sequence of linear programs. Key to achieving an effective algorithm … Read more
This paper approximates simulation models by B-splines with a penalty on high-order finite differences of the coefficients of adjacent B-splines. The penalty prevents overfitting. The simulation output is assumed to be nonnegative. The nonnegative spline simulation metamodel is casted as a second-order cone programming model, which can be solved efficiently by modern optimization techniques. The … Read more
In this paper we propose a new way to compute a warm starting point for a challenging global optimization problem related to Earth imaging in geophysics. The warm start consists of a velocity model that approximately solves a full-waveform inverse problem at low frequency. Our motivation arises from the availability of massively parallel computing platforms … Read more
This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. … Read more
We present a control problem for an electrical vehicle. Its motor can be operated in two discrete modes, leading either to acceleration and energy consumption, or to a recharging of the battery. Mathematically, this leads to a mixed-integer optimal control problem (MIOCP) with a discrete feasible set for the controls taking into account the electrical … Read more
This paper surveys the use of Monte Carlo sampling-based methods for stochastic optimization problems. Such methods are required when—as it often happens in practice—the model involves quantities such as expectations and probabilities that cannot be evaluated exactly. While estimation procedures via sampling are well studied in statistics, the use of such methods in an optimization … Read more
We consider the stochastic economic lot scheduling problem (SELSP) with lost sales and random demand, where switching between products is subject to sequence-dependent setup times. We propose a solution based on simulation optimization using an iterative two-step procedure which combines global policy search with local search heuristics for the traveling salesman sequencing subproblem. To optimize … Read more