Abstract One approach to solving optimal control problems is Bock’s direct multiple shoot- ing method. This method yields lifted nonlinear optimization problems (NLPs) with a spe- cific block structure. Exploiting this structure via tailored optimization algorithms can be computationally beneficial. We propose such methods, primarily within the framework of fil- ter line search sequential quadratic … Read more
Consider the context of solving a multi-objective simulation optimization problem with one or more continuous objective functions to global optimality on a compact feasible set. For a simple algorithm that consists of selecting a finite set of feasible points using a space-filling design, expending the same number of simulation replications at each point to estimate … Read more
The variational inequality (VI) problem is a fundamental mathematical framework for many classical problems. This paper introduces an algorithm that applies to arbitrary finite-dimensional VIs with general compact convex sets and general continuous functions. The algorithm guarantees global linear convergence to an approximate solution without requiring any assumptions, including the typical monotonicity. Our approach adapts … Read more
The primary challenges in systemic risk measurement involve determining an overall reserve level of risk capital and allocating it to different components based on their systemic relevance. In this paper, we introduce a multivariate loss ratio measure (MLRM), which is the minimum amount of capital to be injected into a financial system such that the … Read more
A widely used approximation concept in multiobjective optimization is the concept of enclosures. These are unions of boxes defined by lower and upper bound sets that are used to cover optimal sets of multiobjective optimization problems in the image space. The width of an enclosure is taken as a quality measure. In this paper, we … Read more
Hypervolume is most likely the most often used set quality indicator in (evolutionary) multi-objective optimization. It may be used to compare the quality of solution sets whose images in the objective space are approximations of the true Pareto front. Although in this way we may compare two or more approximations, our knowledge is limited without … Read more
This paper introduces a generalized isotonic optimization framework over an arborescence graph, where each node incurs state-dependent convex costs and a fixed cost upon strict increases. We begin with the special case in which the arborescence is a path and develop a dynamic programming (DP) algorithm with an initial complexity of $O(n^3)$, which we improve … Read more
As countries seek to decarbonize their energy systems, green hydrogen has emerged as a promising energy carrier. This paper studies the production of green hydrogen from offshore wind in the Dutch North Sea, with particular emphasis on understanding how system design decisions and uncertain parameters affect key performance indicators. The analysis builds on a detailed … Read more
Multiobjective optimization is widely used in applications for modeling and solving complex decision-making problems. To help resolve computational and cognitive difficulties associated with problems which have more than three or four objectives, we propose a decomposition and coordination methodology to support decision making for large multiobjective optimization problems (MOPs) with global, quasi-global, and local variables. … Read more
We study a generalization of the classical discrete-time, Linear-Quadratic-Gaussian (LQG) control problem where the noise distributions affecting the states and observations are unknown and chosen adversarially from divergence-based ambiguity sets centered around a known nominal distribution. For a finite horizon model with Gaussian nominal noise and a structural assumption on the divergence that is satisfied … Read more