Linear pencils and quadratic programming problems with a quadratic constraint

2022/01/07 by Santiago Gonzalez Zerbo, Zerbo, Santiago Gonzalez, Alejandra Maestripieri +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2201.02439

openalex publication_date 2022/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given bounded selfadjoint operators A and B acting on a Hilbert space H, consider the linear pencil P(λ)=A+λ B, λ∈ℝ. The set of parameters λ such that P(λ) is a positive (semi)definite operator is characterized. These results are applied to solving a quadratic programming problem with an equality quadratic constraint (or a QP1EQC problem).

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