We present a new algorithm for addressing nonconvex Mixed-Integer Nonlinear Programs (MINLPs) where the cost function is of nonlinear least squares form. We exploit this structure by leveraging a Gauss-Newton quadratic approximation of the original MINLP, leading to the formulation of a Mixed-Integer Quadratic Program (MIQP), which can be solved efficiently. The integer solution of the … Read more
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random variables. It implies, in particular, the necessity of scenario-wise optimality conditions that are behind many fundamental … Read more
Robust controllers that stabilize dynamical systems even under disturbances and noise are often formulated as solutions of nonsmooth, nonconvex optimization problems. While methods such as gradient sampling can handle the nonconvexity and nonsmoothness, the costs of evaluating the objective function may be substantial, making robust control challenging for dynamical systems with high-dimensional state spaces. In … Read more
For the fast approximate solution of Mixed-Integer Non-Linear Programs (MINLPs) arising in the context of Mixed-Integer Optimal Control Problems (MIOCPs) a decomposition algorithm exists that solves a sequence of three comparatively less hard subproblems to determine an approximate MINLP solution. In this work, we propose a problem formulation for the second algorithm stage that is … Read more
The aim of this paper is to formulate several questions related to distributionally robust Stochastic Optimal Control modeling. As an example, the distributionally robust counterpart of the classical inventory model is discussed in details. Finite and infinite horizon stationary settings are considered. Article Download View Distributionally Robust Modeling of Optimal Control
We consider nonlinear optimization problems that involve surrogate models represented by neural net-works. We demonstrate first how to directly embed neural network evaluation into optimization models, highlight a difficulty with this approach that can prevent convergence, and then characterize stationarity of such models. We then present two alternative formulations of these problems in the specific … Read more
In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution … Read more
This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral decomposition for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain. While the theoretical results from the one-dimensional case directly apply to the multidimensional … Read more
We develop Monte-Carlo based heuristic approaches to approximate the objective function in long horizon optimal control problems. In these approaches, to approximate the expectation operator in the objective function, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the average (or weighted average) … Read more
Block tridiagonal systems appear in classic Kalman smoothing problems, as well in generalized Kalman smoothing, where problems may have nonsmooth terms, singular covariance, constraints, nonlinear models, and unknown parameters. In this paper, first we interpret all the classic smoothing algorithms as different approaches to solve positive definite block tridiagonal linear systems. Then, we obtain new … Read more