Topic
Linear inequality
About: Linear inequality is a research topic. Over the lifetime, 3722 publications have been published within this topic receiving 100104 citations. The topic is also known as: linear inequation.
Papers published on a yearly basis
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Papers
Book•
1 Jan 1963
TL;DR: This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Abstract: In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered."The author of this book was the main force in establishing a new mathematical discipline, and he has contributed to its further development at every stage and from every angle. This volume ... is a treasure trove for those who work in this field--teachers, students, and users alike. Its encyclopaedic coverage, due in part to collaboration with other experts, makes it an absolute must."--S. Vajda, Zentralblatt fYr Mathematik und ihre Grenzgebiete
6,155 citations
TL;DR: In this paper, a trust region approach for minimizing nonlinear functions subject to simple bounds is proposed, where the trust region is defined by minimizing a quadratic function subject only to an ellipsoidal constraint and the iterates generated by these methods are always strictly feasible.
Abstract: We propose a new trust region approach for minimizing nonlinear functions subject to simple bounds. By choosing an appropriate quadratic model and scaling matrix at each iteration, we show that it is not necessary to solve a quadratic programming subproblem, with linear inequalities, to obtain an improved step using the trust region idea. Instead, a solution to a trust region subproblem is defined by minimizing a quadratic function subject only to an ellipsoidal constraint. The iterates generated by these methods are always strictly feasible. Our proposed methods reduce to a standard trust region approach for the unconstrained problem when there are no upper or lower bounds on the variables. Global and quadratic convergence of the methods is established; preliminary numerical experiments are reported.
3,497 citations
TL;DR: A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules.
3,274 citations
Journal Article•
TL;DR: In this article, the authors present a systematic treatment of the conceptual framework as well as the practical problems of measurement of inequality, and evaluate alternative approaches in terms of their philosophical assumptions, economic content, and statistical requirements.
Abstract: First published in 1973, this book presents a systematic treatment of the conceptual framework as well as the practical problems of measurement of inequality. Alternative approaches are evaluated in terms of their philosophical assumptions, economic content, and statistical requirements. In a new introduction, Amartya Sen, jointly with James Foster, critically surveys the literature that followed the publication of this book, and also evaluates the main analytical issues in the appraisal of economic inequality and poverty.
2,584 citations
TL;DR: An alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities is proposed and it is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions.
2,159 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 4 |
| 2024 | 11 |
| 2023 | 9 |
| 2022 | 16 |
| 2021 | 70 |
| 2020 | 84 |