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Lagrangian Duality in Convex Conic Programming with Simple Proofs
In this paper, we study Lagrangian duality aspects in convex conic programming over general convex cones. It is known that the duality in convex...
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A Lagrangian bounding and heuristic principle for bi-objective discrete optimization
Lagrangian relaxation is a common and often successful way to approach computationally challenging single-objective discrete optimization problems...
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Separable Lagrangian Decomposition for Quasi-Separable Problems
Lagrangian relaxation is a powerful technique that applies when the removal of some appropriately chosen set of “complicating” constraints makes a(n...
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Survey on Lagrangian relaxation for MILP: importance, challenges, historical review, recent advancements, and opportunities
Operations in areas of importance to society are frequently modeled as mixed-integer linear programming (MILP) problems. While MILP problems suffer...
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A Lagrangian relaxation approach to an electricity system investment model with a high temporal resolution
The global production of electricity contributes significantly to the release of carbon dioxide emissions. Therefore, a transformation of the...
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Local Duality and Dual Methods
We first derive a local duality theory for constrained nonconvex optimization, which is based on our earlier global duality theory and the Lagrangian...
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A Feasibility-Ensured Lagrangian Heuristic for General Decomposable Problems
The Lagrangian relaxation method is a popular and useful tool to solve large-scale optimization problems with decomposable structures. A drawback of...
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Convex Optimization: Saddle Points Characterization and Introduction to Duality
In the last 50 years or more, the words “nonsmooth optimization” generally refer to nonlinear programming problems (or also to problems of calculus...
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Decomposition Methods for Choice-Based Optimization Models
Transportation and mobility service providers face challenges when designing their services to ensure that resources align with demand effectively....
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Duality Theory
Associated with every linear program is another called its dual. The dual of this dual linear program is the original linear program (which is then...
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A Dissection of the Duality Gap of Set Covering Problems
Set covering problems are well-studied and have many applications. Sometimes the duality gap is significant and the problem is computationally...
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On supply and network investment in power systems
In this work we discuss the question of investment in power systems wherein the need for flexibility would be a driving force for investments. The...
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On the Principle of Lagrange in Optimization Theory and Its Application in Transportation and Location Problems
In mathematical optimization, the Lagrangian approach is a general method to find an optimal solution of a finite (infinite) dimensional constrained...
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A Lagrangian relaxation algorithm for optimizing a bi-objective agro-supply chain model considering CO2 emissions
In this research, an agro-supply chain in the context of both economic and environmental issues has been investigated. To this end, a bi-objective...
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Applying available-to-promise (ATP) concept in mixed-model assembly line sequencing problems in a Make-To-Order (MTO) environment: problem extension, model formulation and Lagrangian relaxation algorithm
Mixed-model assembly line is known to be a special case of production lines where variety of product models similar to product characteristics are...
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Enhanced capacitated facility location problem for mental accounting management using partial resource concentration
This paper studies a framework of Reliable Capacitated Facility Location Problem with Single source constraint, which allows us to capture the mental...
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Continuous Constrained Optimization
This chapter presents the necessary and sufficient conditions for the local and global optimality of continuous, constrained optimization problems...
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The robust multi-plant capacitated lot-sizing problem
In this paper, we study the robust multi-plant capacitated lot-sizing problem with uncertain demands, processing and setup times. This problem...
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Order assignment in a ride-hailing platform with heterogeneous participants
We study an order assignment problem in a ride-hailing system with two classes of riders (i.e., single-choice riders and multi-choice riders) and n ...
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Robust maximum flow network interdiction considering uncertainties in arc capacity and resource consumption
This article discusses a robust network interdiction problem considering uncertainties in arc capacities and resource consumption. The problem...
