Related papers: Necessary and sufficient conditions for Pareto eff…

Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we…

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…

This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…

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…

Deep learning models form one of the most powerful machine learning models for the extraction of important features. Most of the designs of deep neural models, i.e., the initialization of parameters, are still manually tuned. Hence,…

This paper is divided to two parts. In the first part, we provide elementary proofs for some important results in multi-objective optimization. The given proofs are so simple and short in compared to the existing ones. Also, a Pareto…

Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

A multiobjective optimization problem is simplicial if the Pareto set and front are homeomorphic to a simplex and, under the homeomorphisms, each face of the simplex corresponds to the Pareto set and front of a subproblem. In this paper, we…

The rapid uptake of renewable energy sources in the electricity grid leads to a demand in load shaping and flexibility. Energy storage devices such as batteries are a key element to provide solutions to these tasks. However, typically a…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly. We explore the limitations of higher-order optimization and prove that even for convex optimization,…

In power systems, large-scale optimisation problems are extensively used to plan for capacity expansion at the supra-national level. However, their cost-optimal solutions are often not exploitable by decision-makers who are preferably…

In this article we develop a gradient-based algorithm for the solution of multiobjective optimization problems with uncertainties. To this end, an additional condition is derived for the descent direction in order to account for…

We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…

In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice. We estimate all parameters, the strength of the objects and the boundaries of equal decision,…

The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…

This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…

It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…