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Partial Integral Equations (PIEs) have been used to represent both systems with delay and systems of Partial Differential Equations (PDEs) in one or two spatial dimensions. In this paper, we show that these results can be combined to obtain…

Many science and engineering applications require finding solutions to planning and optimization problems by satisfying a set of constraints. These constraint problems (CPs) are typically NP-complete and can be formalized as constraint…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…

With the growing access to administrative health databases, retrospective studies have become crucial evidence for medical treatments. Yet, non-randomized studies frequently face selection biases, requiring mitigation strategies. Propensity…

Interference Alignment (IA) is technique that, in a large sense, makes use of the increasing signal dimensions available in the system through MIMO and OFDM technologies in order to globally reduce the interference suffered by users in a…

Intermittent Androgen Suppression (IAS) is a treatment strategy for delaying or even preventing time to relapse of advanced prostate cancer. IAS consists of alternating cycles of therapy (in the form of androgen suppression) and…

Multiple operational constraints of power system stability are derived analytically and reformulated into Second-Order Cone (SOC) form through a unification method in Part I of this paper. The accuracy and conservativeness of the proposed…

The state transition algorithm (STA), as an intelligent optimization method grounded in constructivist learning, has been demonstrated to be highly effective in solving complex optimization problems. However, the standard STA suffers from…

We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the…

End-to-end motion planning is promising for simplifying complex autonomous driving pipelines. However, challenges such as scene understanding and effective prediction for decision-making continue to present substantial obstacles to its…

PID controllers are widely used in control systems because of their simplicity and effectiveness. Although advanced optimization techniques such as Bayesian Optimization and Differential Evolution have been applied to address the challenges…

Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…

The increased dominance of intra-die process variations has motivated the field of Statistical Static Timing Analysis (SSTA) and has raised the need for SSTA-based circuit optimization. In this paper, we propose a new sensitivity based,…

Minimising cycle time without inducing quality defects is a major challenge in the injection moulding (IM). Design of Experiment methods (DoE) have been widely studied for optimisation of the IM, however existing methods have limitations,…

In this paper, we study age of information (AoI) optimization for status updating in an integrated sensing and communication (ISAC) system. We consider a discrete-time architecture in which a base station interacts with a physical…

Traditional language models, adept at next-token prediction in text sequences, often struggle with transduction tasks between distinct symbolic systems, particularly when parallel data is scarce. Addressing this issue, we introduce…

We present a new Partial Integral Equation (PIE) representation of Partial Differential Equations (PDEs) in which it is possible to use convex optimization to perform stability analysis with little or no conservatism. The first result gives…

Recent studies show that advanced priors play a major role in deep generative models. Exemplar VAE, as a variant of VAE with an exemplar-based prior, has achieved impressive results. However, due to the nature of model design, an…

This paper focuses on developing energy-efficient online data processing strategy of wireless powered MEC systems under stochastic fading channels. In particular, we consider a hybrid access point (HAP) transmitting RF energy to and…