Related papers: Approximation of a Pareto Set Segment Using a Line…
Bilevel optimization problems comprise an upper level optimization task that contains a lower level optimization task as a constraint. While there is a significant and growing literature devoted to solving bilevel problems with single…
In this paper, we propose a simple global optimisation algorithm inspired by Pareto's principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the…
Given a graph $G$, the NP-hard Maximum Planar Subgraph problem (MPS) asks for a planar subgraph of $G$ with the maximum number of edges. There are several heuristic, approximative, and exact algorithms to tackle the problem, but---to the…
Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…
Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic…
In this paper, we are interested in the existence of Pareto solutions to vector polynomial optimization problems over a basic closed semi-algebraic set. By invoking some powerful tools from real semi-algebraic geometry, we first introduce…
We provide a sparse version of the bounded degree SOS hierarchy BSOS [7] for polynomial optimization problems. It permits to treat large scale problems which satisfy a structured sparsity pattern. When the sparsity pattern satisfies the…
We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…
This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by…
This manuscript introduces an autotuned algorithm for searching nearest neighbors based on neighbor graphs and optimization metaheuristics to produce Pareto-optimal searches for quality and search speed automatically; the same strategy is…
This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…
Pareto optimization using evolutionary multi-objective algorithms has been widely applied to solve constrained submodular optimization problems. A crucial factor determining the runtime of the used evolutionary algorithms to obtain good…
In several applications, input samples are more naturally represented in terms of similarities between each other, rather than in terms of feature vectors. In these settings, machine-learning algorithms can become very computationally…
We study the problem of finding the best linear model that can minimize least-squares loss given a data-set. While this problem is trivial in the low dimensional regime, it becomes more interesting in high dimensions where the population…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
To find efficient screening methods for high dimensional linear regression models, this paper studies the relationship between model fitting and screening performance. Under a sparsity assumption, we show that a subset that includes the…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
In multi-objective optimization, the set of optimal trade-offs -- the Pareto front -- often contains regions that are extremely steep or flat. The Pareto optimal points in these regions are typically of limited interest for decision-making,…
Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…