We consider a setting in which it is desired to find an optimal complex vector ∈ that satisfies () ≈ in a least-squares sense, where ∈ is a data vector (possibly noise-corrupted), and (·) : → is a measurement operator. If (·) were linear, this reduces to the classical linear least-squares problem, which has a well-known analytic solution as well as powerful iterative solution algorithms. However, instead of linear least-squares, this work considers the more complicated scenario where (·) is nonlinear, but can be represented as the summation and/or composition of some operators that are linear and some operators that are antilinear. Some common nonlinear operations that have this structure include complex conjugation or taking the real-part or imaginary-part of a complex vector. Previous literature has shown that this kind of mixed linear/antilinear least-squares problem can be mapped into a linear least-squares problem by considering as a vector in instead of . While this approach is valid, the replacement of the original complex-valued optimization problem with a real-valued optimization problem can be complicated to implement, and can also be associated with increased computational complexity. In this work, we describe theory and computational methods that enable mixed linear/antilinear least-squares problems to be solved iteratively using standard linear least-squares tools, while retaining all of the complex-valued structure of the original inverse problem. An illustration is providedtodemonstratethatthisapproachcansimplifytheimplementationandreduce the computational complexity of iterative solution algorithms.

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.

Global warming and climate change call for urgent minimization of the impact of human activities on the environment. There is a great need for the improvement of resource efficiencies by integrating various life-supporting systems. The challenge is on the energy, water and environment systems to integrate and become more sustainable. This research field has received increased attention over the past years with studies across the energy, water and environment systems that optimized different engineering problems. The present Special Issue stems from four Conferences on Sustainable Development of Energy, Water and Environment Systems held in 2020, in four countries of three continents. This review introduction article intends to introduce the topical field and the articles included in this Special Issue of Optimization and Engineering.

This paper proposes a general-purpose multi-agent Bayesian optimization (MABO) where agents are connected via shared variables or constraints, and each agent's local cost is unknown. The proposed approach is general-purpose in the sense that it can be used with a broad class of decomposition methods, whereby we augment traditional BO acquisition functions with suitably derived coordinating terms to facilitate coordination among subsystems without sharing local data. Regret analysis is also carried out for the general-purpose MABO framework, which reveals that the cumulative regret of the proposed general-purpose MABO is the sum of individual regrets and is independent of the coordinating terms. This adaptability to different decomposition methods ensures versatility across diverse distributed optimization scenarios. Numerical experiments validate the effectiveness of the proposed MABO framework for different classes of decomposition methods.