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Interior-Point Algorithms For A Class Of Convex Optimization Problems, Goran Lesaja, Verlynda Slaughter
Interior-Point Algorithms For A Class Of Convex Optimization Problems, Goran Lesaja, Verlynda Slaughter
Department of Mathematical Sciences Faculty Publications
In this paper we consider interior-point methods (IPM) for the nonlinear, convex optimization problem where the objective function is a weighted sum of reciprocals of variables subject to linear constraints (SOR). This problem appears often in various applications such as statistical stratified sampling and entropy problems, to mention just few examples. The SOR is solved using two IPMs. First, a homogeneous IPM is used to solve the Karush-Kuhn-Tucker conditions of the problem which is a standard approach. Second, a homogeneous conic quadratic IPM is used to solve the SOR as a reformulated conic quadratic problem. As far as we are …
Introducing Interior-Point Methods For Introductory Operations Research Courses And/Or Linear Programming Courses, Goran Lesaja
Introducing Interior-Point Methods For Introductory Operations Research Courses And/Or Linear Programming Courses, Goran Lesaja
Department of Mathematical Sciences Faculty Publications
In recent years the introduction and development of Interior-Point Methods has had a profound impact on optimization theory as well as practice, influencing the field of Operations Research and related areas. Development of these methods has quickly led to the design of new and efficient optimization codes particularly for Linear Programming. Consequently, there has been an increasing need to introduce theory and methods of this new area in optimization into the appropriate undergraduate and first year graduate courses such as introductory Operations Research and/or Linear Programming courses, Industrial Engineering courses and Math Modeling courses. The objective of this paper is …