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The rapid development of cloud-native architecture has promoted the widespread application of container technology, but the optimization problems in container scheduling and resource management still face many challenges. This paper…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
In this paper, we propose an inexact Augmented Lagrangian Method (ALM) for the optimization of convex and nonsmooth objective functions subject to linear equality constraints and box constraints where errors are due to fixed-point data. To…
There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
Electric machine design optimization is a computationally expensive multi-objective optimization problem. While the objectives require time-consuming finite element analysis, optimization constraints can often be based on mathematical…
Solving optimization problems on quantum annealers usually requires each variable of the problem to be represented by a connected set of qubits called a logical qubit or a chain. Chain weights, in the form of ferromagnetic coupling between…
This study addresses the difficulties associated with inventory management of products with stochastic demand. The objective is to find the optimal combination of order quantity and reorder point that maximizes profit while considering…
Training of neural networks amounts to nonconvex optimization problems that are typically solved by using backpropagation and (variants of) stochastic gradient descent. In this work we propose an alternative approach by viewing the training…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
Most recently, He and Yuan [arXiv:2108.08554, 2021] have proposed a balanced augmented Lagrangian method (ALM) for the canonical convex programming problem with linear constraints, which advances the original ALM by balancing its…
This work addresses the uniform parallel machine scheduling problem within an optimistic bilevel optimization framework. The leader seeks to minimize the weighted number of tardy jobs, while the follower aims to minimize the total…
New architectures and algorithms are needed to reflect the mixture of local and global information that is available as multi-agent systems connect over the cloud. We present a novel architecture for multi-agent coordination where the cloud…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
There is a growing need to integrate sustainability into tertiary mathematics education given the urgency of addressing global environmental challenges. This paper presents four case studies from Australian university courses that…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and…
Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power procurement schedule to minimize operating…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
This paper studies a stochastic algorithm for linearly constrained nonconvex optimization, where the objective function is smooth but only unbiased stochastic gradients with bounded variance are available. We propose a momentum-based…