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Achieving long-term stable optimization in complex industrial processes (CIPs) is notoriously challenging due to their unclear physical/chemical reaction mechanisms, fluctuating operating conditions, and stringent regulatory constraints. A significant gap persists between promising artificial intelligence (AI) algorithms developed in academic research and their practical deployment in industrial actual processes. To bridge this gap, this article introduces the AI- and security-empowered end–edge–cloud modular platform (AISE3CMP). It consists of four systems such as whole-process AI modeling, end-side basic loop and AI-assisted decision-making, edge-side security isolation and AI control, and cloud-side security transmission and AI optimization. The data isolation collection module of the platform was deployed at a municipal solid waste incineration (MSWI) power plant in Beijing, where it collected multimodal data from real-world industrial sites. The platform’s functionality and effectiveness were validated through the software and hardware developed at the Smart Environmental Protection Beijing Laboratory. The experimental results show efficient and reliable signal transmission between the systems, confirming the platform’s ability to meet the computational demands of AI-based optimization and control algorithms. Compared to previous platforms, AISE3CMP features a dual-security transmission mechanism to mitigate data exchange risks and a modular design to enhance integration efficiency. To the best of our knowledge, this platform is the first prototype of a portable, end-to-end cloud platform with a dual-layer security mechanism for CIPs. While the platform effectively addresses data transmission security, further strengthening of cloud-side data protection and ensuring operational safety on the end-side remain significant challenges for the future. Additionally, utilizing this architecture to enable multi-region and multi-plant data sharing, in order to develop industry-specific large language models, represents a key research direction.

Focusing on the power consumption of a regional multi-energy system with the characteristics of energy congestion in students’ dormitory buildings in the hot summer and warm winter regions of southern China, a practical regional multi-energy system consisting of three subsystems, namely an integrated screw chiller (ISC), a screw ground-source heat pump (SGSHP), and an air-source heat pump (ASHP), was optimised by the operation control strategy. The system’s power consumption and cooling/heating load characteristics during operation were analysed, and changes in the terminal air-conditioning load were simulated. Based on the dynamic cooling and heating load of the building, a two-stage loading strategy was proposed for optimising the system operation. Taking the load demand matching requirement of the system output and the terminal load demand as constraints, a simulation model of the system was developed using TRNSYS 16 software, and the changes in power consumption and the cooling/heating capacity before and after optimisation were analysed. The results show that the optimised system reduced annual power consumption by approximately 19% and increased condensation heat recovery by about 2.3%. The optimised operation control strategy was aligned well with the terminal cooling and heating demands.

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee whenever the constraints and objective function are concave in the uncertainty. We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queueing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data are available.

In view of the minimization of a nonsmooth nonconvex function f , we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka–Łojasiewicz inequality. This assumption allows to cover a wide range of problems, including nonsmooth semi-algebraic (or more generally tame) minimization. The specialization of our result to different kinds of structured problems provides several new convergence results for inexact versions of the gradient method, the proximal method, the forward–backward splitting algorithm, the gradient projection and some proximal regularization of the Gauss–Seidel method in a nonconvex setting. Our results are illustrated through feasibility problems, or iterative thresholding procedures for compressive sensing.

Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject.

In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two terms: one is smooth and given by a black-box oracle, and another is a simple general convex function with known structure. Despite the absence of good properties of the sum, such problems, both in convex and nonconvex cases, can be solved with efficiency typical for the first part of the objective. For convex problems of the above structure, we consider primal and dual variants of the gradient method (with convergence rate ), and an accelerated multistep version with convergence rate , where is the iteration counter. For nonconvex problems with this structure, we prove convergence to a point from which there is no descent direction. In contrast, we show that for general nonsmooth, nonconvex problems, even resolving the question of whether a descent direction exists from a point is NP-hard. For all methods, we suggest some efficient “line search” procedures and show that the additional computational work necessary for estimating the unknown problem class parameters can only multiply the complexity of each iteration by a small constant factor. We present also the results of preliminary computational experiments, which confirm the superiority of the accelerated scheme.

We analyze the stochastic average gradient (SAG) method for optimizing the sum of a finite number of smooth convex functions. Like stochastic gradient (SG) methods, the SAG method’s iteration cost is independent of the number of terms in the sum. However, by incorporating a memory of previous gradient values the SAG method achieves a faster convergence rate than black-box SG methods. The convergence rate is improved from O ( 1 / k ) to O (1 /  k ) in general, and when the sum is strongly-convex the convergence rate is improved from the sub-linear O (1 /  k ) to a linear convergence rate of the form O ( ρ k ) for ρ < 1 . Further, in many cases the convergence rate of the new method is also faster than black-box deterministic gradient methods, in terms of the number of gradient evaluations. This extends our earlier work Le Roux et al. (Adv Neural Inf Process Syst, 2012 ), which only lead to a faster rate for well-conditioned strongly-convex problems. Numerical experiments indicate that the new algorithm often dramatically outperforms existing SG and deterministic gradient methods, and that the performance may be further improved through the use of non-uniform sampling strategies.

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., the problem min x E v f v ( E w [ g w ( x ) ] ) . In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasi-gradient method. SCGD update the solutions based on noisy sample gradients of f v , g w and use an auxiliary variable to track the unknown quantity E w g w ( x ) . We prove that the SCGD converge almost surely to an optimal solution for convex optimization problems, as long as such a solution exists. The convergence involves the interplay of two iterations with different time scales. For nonsmooth convex problems, the SCGD achieves a convergence rate of O ( k - 1 / 4 ) in the general case and O ( k - 2 / 3 ) in the strongly convex case, after taking k samples. For smooth convex problems, the SCGD can be accelerated to converge at a rate of O ( k - 2 / 7 ) in the general case and O ( k - 4 / 5 ) in the strongly convex case. For nonconvex problems, we prove that any limit point generated by SCGD is a stationary point, for which we also provide the convergence rate analysis. Indeed, the stochastic setting where one wants to optimize compositions of expected-value functions is very common in practice. The proposed SCGD methods find wide applications in learning, estimation, dynamic programming, etc.

Efficient global optimization (EGO) is the canonical form of Bayesian optimization that has been successfully applied to solve global optimization of expensive-to-evaluate black-box problems. However, EGO struggles to scale with dimension, and offers limited theoretical guarantees. In this work, a trust-region framework for EGO (TREGO) is proposed and analyzed. TREGO alternates between regular EGO steps and local steps within a trust region. By following a classical scheme for the trust region (based on a sufficient decrease condition), the proposed algorithm enjoys global convergence properties, while departing from EGO only for a subset of optimization steps. Using extensive numerical experiments based on the well-known COCO bound constrained problems, we first analyze the sensitivity of TREGO to its own parameters, then show that the resulting algorithm is consistently outperforming EGO and getting competitive with other state-of-the-art black-box optimization methods.