Related papers: Large-scale matrix optimization based multi microg…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
This paper proposes the method to optimize restriction and prolongation operators in the two-grid method. The proposed method is straightforwardly extended to the geometric multigrid method (GMM). GMM is used in solving discretized partial…
In this paper, we propose an efficient semidefinite programming (SDP) approach to worst-case linear discriminant analysis (WLDA). Compared with the traditional LDA, WLDA considers the dimensionality reduction problem from the worst-case…
An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…
Many real-world optimisation problems involve multiple objectives. When considered concurrently, they give rise to a set of optimal trade-off solutions, also known as efficient solutions. These solutions have the property that neither…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
We revisit the problem of large-scale assortment optimization under the multinomial logit choice model without any assumptions on the structure of the feasible assortments. Scalable real-time assortment optimization has become essential in…
This paper addresses the optimal control problem of finite-horizon discrete-time nonlinear systems under state and control constraints. A novel numerical algorithm based on optimal control theory is proposed to achieve superior…
We consider the central role of improving directions in solution methods for mixed integer bilevel linear optimization problems (MIBLPs). Current state-of-the-art methods for solving MIBLPs employ the branch-and-cut framework originally…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
Topology optimization problems often support multiple local minima due to a lack of convexity. Typically, gradient-based techniques combined with continuation in model parameters are used to promote convergence to more optimal solutions;…
We define very large-scale multiobjective optimization problems as optimizing multiple objectives (VLSMOPs) with more than 100,000 decision variables. These problems hold substantial significance, given the ubiquity of real-world scenarios…
Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems,…
Despite recent progress in constructing generalizable parallel algorithm portfolios (PAPs), no general-purpose approach is yet available for multi-objective binary optimization problems (MOBOPs). To fill this gap, this paper proposes…
The application of Large Language Models (LLMs) for Automated Algorithm Discovery (AAD), particularly for optimisation heuristics, is an emerging field of research. This emergence necessitates robust, standardised benchmarking practices to…
This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first…
In this letter, we introduce a novel pilot design approach that minimizes the total mean square errors of the minimum mean square error estimators of all base stations (BSs) subject to the transmit power constraints of individual users in…
Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose…
We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…