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How Technology Has Changed What It Means to Think Mathematically
For thousands of years, mastering numerical and symbolic calculation techniques was essential to be able to do mathematics. By 1990, that requirement...
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Computation of Optimal Transport and Related Hedging Problems via Penalization and Neural Networks
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks....
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Main Components of Mathematical Models
In the previous chapter, the main components of a mathematical model (decision variables, constraints, objective function, and parameters) were...
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Dual representations for systemic risk measures
The financial crisis showed the importance of measuring, allocating and regulating systemic risk. Recently, the systemic risk measures that can be...
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Commentaries and Further Developments
In this chapter, we comment on and discuss some of the most important further developments obtained in the domains considered. More extensions are...
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Diagnosability analysis of patterns on bounded labeled prioritized Petri nets
Checking the diagnosability of a discrete event system aims at determining whether a fault can always be identified with certainty after the...
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Quantum state tomography with time-continuous measurements: reconstruction with resource limitations
We propose and analyze quantum state estimation (tomography) using continuous quantum measurements with resource limitations, allowing the global...
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Optimization of black-box problems using Smolyak grids and polynomial approximations
A surrogate-based optimization method is presented, which aims to locate the global optimum of box-constrained problems using input–output data. The...
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Proof Verification Technology and Elementary Physics
Software technology that can be used to validate the logical correctness of mathematical proofs has attained a high degree of power and...
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Clustering I: Basic Clustering Models and Algorithms
Clustering is an unsupervised classification technique that identifies some inherent structure present in a set of objects based on a similarity...
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Robust return risk measures
In this paper we provide an axiomatic foundation to Orlicz risk measures in terms of properties of their acceptance sets, by exploiting their natural...
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A stochastic optimization formulation for the transition from open pit to underground mining
As open pit mining of a mineral deposit deepens, the cost of extraction may increase up to a threshold where transitioning to mining through...
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Dynamic portfolio choice: a simulation-and-regression approach
Simulation-and-regression algorithms have become a standard tool for solving dynamic programs in many areas, in particular financial engineering and...
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Decision Making When Consequences Are Random
The intricacy of decision making is often due to uncertainty about the data to base a decision upon, and the consequences that the decision implies....
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Optimization of PDEs with Uncertain Inputs
Uncertainty pervades nearly all science and engineering applications including the optimal control and design of systems governed by partial...
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Set-valued loss-based risk measures
In this paper, we introduce a new class of set-valued risk measures, named set-valued convex loss-based risk measures. Representation results are...
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Asynchronous Coordination of Distributed Energy Resources with Packetized Energy Management
To enable greater penetration of renewable energy, there is a need to move away from the traditional form of ensuring electric grid reliability...
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Efficient Fuzzy Goal Programming Model for Multi-objective Production Distribution Problem
This paper comprises of modelling and optimization of a production–distribution problem with the multi-product. The proposed model combined three...
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Concept Development
Concept design involves develo** a selected architectural design in a more concrete and detailed fashion. This may make it necessary to make...
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Solving Dynamic Portfolio Choice Models in Discrete Time Using Spatially Adaptive Sparse Grids
In this paper, I propose a dynamic programming approach with value function iteration to solve Bellman equations in discrete time using spatially...