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Extending the idea of Even and Lehrer [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of…
Most existing studies on evolutionary multi-objective optimization focus on approximating the whole Pareto-optimal front. Nevertheless, rather than the whole front, which demands for too many points (especially in a high-dimensional space),…
Deep neural networks achieve state-of-the-art and sometimes super-human performance across various domains. However, when learning tasks sequentially, the networks easily forget the knowledge of previous tasks, known as "catastrophic…
In this paper we consider the problem of learning variational models in the context of supervised learning via risk minimization. Our goal is to provide a deeper understanding of the two approaches of learning of variational models via…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Two-phase methods are commonly used to solve bi-objective combinatorial optimization problems. In the first phase, all extreme supported nondominated points are generated through a dichotomic search. This phase also allows the…
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the proposed method through the employment of multiple interacting…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Chance constraints are a valuable tool for the design of safe decisions in uncertain environments; they are used to model satisfaction of a constraint with a target probability. However, because of possible non-convexity and non-smoothness,…
Gradient-based hyperparameter optimization (HPO) have emerged recently, leveraging bilevel programming techniques to optimize hyperparameter by estimating hypergradient w.r.t. validation loss. Nevertheless, previous theoretical works mainly…
Many real-world optimization problems such as engineering design can be eventually modeled as the corresponding multiobjective optimization problems (MOPs) which must be solved to obtain approximate Pareto optimal fronts. Multiobjective…
Optimization for deep networks is currently a very active area of research. As neural networks become deeper, the ability in manually optimizing the network becomes harder. Mini-batch normalization, identification of effective respective…
Data rebalancing techniques, including oversampling and undersampling, are a common approach to addressing the challenges of imbalanced data. To tackle unresolved problems related to both oversampling and undersampling, we propose a new…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…
Submodular functions allow to model many real-world optimisation problems. This paper introduces approaches for computing diverse sets of high quality solutions for submodular optimisation problems. We first present diversifying greedy…
Bi-Level Optimization (BLO) is originated from the area of economic game theory and then introduced into the optimization community. BLO is able to handle problems with a hierarchical structure, involving two levels of optimization tasks,…
In this paper, we propose a combined approach with second-order optimality conditions of the lower level problem to study constraint qualifications and optimality conditions for bilevel programming problems. The new method is inspired by…
When applying optimization method to a real-world problem, the possession of prior knowledge and preliminary analysis on the landscape of a global optimization problem can give us an insight into the complexity of the problem. This…
In this work we consider multitasking in the context of solving multiple optimization problems simultaneously by conducting a single search process. The principal goal when dealing with this scenario is to dynamically exploit the existing…