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Given the high computational cost of preference alignment training of large language models (LLMs), exploring efficient methods to reduce the training overhead remains an important and compelling research problem. Motivated by the…
Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the…
Topology optimization is one of the engineering tools for finding efficient design. For the material interpolation scheme, it is usual to employ the SIMP (Solid Isotropic Material with Penalization) or the homogenization based interpolation…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
Recent advances in high refresh rate displays as well as the increased interest in high rate of slow motion and frame up-conversion fuel the demand for efficient and cost-effective multi-frame video interpolation solutions. To that regard,…
This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…
In this paper, a new one-parameter filled function approach is developed for nonlinear multi-objective optimization. Inspired by key filled function ideas from single-objective optimization, the proposed method is adapted to the…
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
This paper addresses the challenge of developing efficient algorithms for large-scale nonconvex multiobjective optimization problems (MOPs). While quasi-Newton methods are effective, their traditional application to MOPs is computationally…
In this paper, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding)…
Multi-fidelity simulation is a widely used strategy to reduce the computational cost of many-query numerical simulation tasks such as uncertainty quantification, design space exploration, and design optimization. The reduced basis approach…
In this paper, we consider a class of nonsmooth nonconvex optimization problems whose objective is the sum of a block relative smooth function and a proper and lower semicontinuous block separable function. Although the analysis of block…
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…
Treating high dimensionality is one of the main challenges in the development of computational methods for solving problems arising in finance, where tasks such as pricing, calibration, and risk assessment need to be performed accurately…
To address the problem of combined heat and power economic emission dispatch (CHPEED), a two-stage approach is proposed by combining multi-objective optimization (MOO) with integrated decision making (IDM). First, a practical CHPEED model…
We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that…
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, the…
This paper presents new fast algorithms for Hermite interpolation and evaluation over finite fields of characteristic two. The algorithms reduce the Hermite problems to instances of the standard multipoint interpolation and evaluation…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…