Related papers: A variational geometric framework for multi-object…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

This work considers a multiobjective version of the unit commitment problem that deals with finding the optimal generation schedule of a firm, over a period of time and a given electrical network. With growing importance of environmental…

In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks…

A multi-modal multi-objective optimization problem is a special kind of multi-objective optimization problem with multiple Pareto subsets. In this paper, we propose an efficient multi-modal multi-objective optimization algorithm based on…

A probabilistic graphical model is proposed, modeling the joint model parameter and multiplier evolution, with a hypervolume based likelihood, promoting multi-objective descent in structural risk minimization. We address multi-objective…

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…

Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…

Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…

A traditional and intuitively appealing Multi-Task Multiple Kernel Learning (MT-MKL) method is to optimize the sum (thus, the average) of objective functions with (partially) shared kernel function, which allows information sharing amongst…

We propose here the use of the variational level set methodology to capture Lagrangian vortex boundaries in 2D unsteady velocity fields. This method reformulates earlier approaches that seek material vortex boundaries as extremum solutions…

We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…

This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization…

To date, the multi-objective optimization literature has mainly focused on conflicting objectives, studying the Pareto front, or requiring users to balance tradeoffs. Yet, in machine learning practice, there are many scenarios where such…

In this paper, we propose a unifying framework incorporating several momentum-related search directions for solving strongly monotone variational inequalities. The specific combinations of the search directions in the framework are made to…

Efficiently solving multi-objective optimization problems for simulation optimization of important scientific and engineering applications such as materials design is becoming an increasingly important research topic. This is due largely to…

Geometric programming problems occur frequently in engineering design and management. In multiobjective optimization, the trade-off information between different objective functions is probably the most important piece of information in a…

Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but…

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…

This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…

Prior work in multi-objective reinforcement learning typically uses linear reward scalarization with fixed weights, which provably fails to capture non-convex Pareto fronts and thus yields suboptimal results. This limitation becomes…