A matroid algorithm and its application to the efficient solution of two optimization problems on graphs

1988 ◽  
Vol 42 (1-3) ◽  
pp. 471-487 ◽  
Author(s):  
Carl Brezovec ◽  
Gérard Cornuéjols ◽  
Fred Glover
Keyword(s):  
Efficient Solution ◽  
Optimization Problems

From Optimization to Clustering

2015 ◽  
pp. 594-619 ◽  
Author(s):  
Megha Vora ◽  
T. T. Mirnalinee
Keyword(s):  
Particle Swarm Optimization ◽  
Swarm Intelligence ◽  
Optimization Algorithm ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimization Techniques ◽  
Ant Colony Optimization Algorithm ◽  
Swarm Optimization ◽  
Insight Into

In the past two decades, Swarm Intelligence (SI)-based optimization techniques have drawn the attention of many researchers for finding an efficient solution to optimization problems. Swarm intelligence techniques are characterized by their decentralized way of working that mimics the behavior of colony of ants, swarm of bees, flock of birds, or school of fishes. Algorithmic simplicity and effectiveness of swarm intelligence techniques have made it a powerful tool for solving global optimization problems. Simulation studies of the graceful, but unpredictable, choreography of bird flocks led to the design of the particle swarm optimization algorithm. Studies of the foraging behavior of ants resulted in the development of ant colony optimization algorithm. This chapter provides insight into swarm intelligence techniques, specifically particle swarm optimization and its variants. The objective of this chapter is twofold: First, it describes how swarm intelligence techniques are employed to solve various optimization problems. Second, it describes how swarm intelligence techniques are efficiently applied for clustering, by imposing clustering as an optimization problem.

From Optimization to Clustering

2016 ◽  
pp. 1519-1544 ◽  
Author(s):  
Megha Vora ◽  
T. T. Mirnalinee
Keyword(s):  
Particle Swarm Optimization ◽  
Swarm Intelligence ◽  
Optimization Algorithm ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimization Techniques ◽  
Ant Colony Optimization Algorithm ◽  
Swarm Optimization ◽  
Insight Into

In the past two decades, Swarm Intelligence (SI)-based optimization techniques have drawn the attention of many researchers for finding an efficient solution to optimization problems. Swarm intelligence techniques are characterized by their decentralized way of working that mimics the behavior of colony of ants, swarm of bees, flock of birds, or school of fishes. Algorithmic simplicity and effectiveness of swarm intelligence techniques have made it a powerful tool for solving global optimization problems. Simulation studies of the graceful, but unpredictable, choreography of bird flocks led to the design of the particle swarm optimization algorithm. Studies of the foraging behavior of ants resulted in the development of ant colony optimization algorithm. This chapter provides insight into swarm intelligence techniques, specifically particle swarm optimization and its variants. The objective of this chapter is twofold: First, it describes how swarm intelligence techniques are employed to solve various optimization problems. Second, it describes how swarm intelligence techniques are efficiently applied for clustering, by imposing clustering as an optimization problem.

scholarly journals Continuous-Time Multiobjective Optimization Problems via Invexity

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Valeriano A. De Oliveira ◽  
Marko A. Rojas-Medar
Keyword(s):  
Continuous Time ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Weakly Efficient Solution ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Multiobjective Programming Problems

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.

On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems

2020 ◽  
pp. 2050040
Author(s):  
Le Thanh Tung
Keyword(s):  
Vector Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Second Order ◽  
Vector Optimization Problems ◽  
Solution Maps ◽  
Qualification Conditions ◽  
Parametric Vector Optimization ◽  
Perturbation Maps ◽  
Proper Efficient Solution

The main aim of this paper is to study second-order sensitivity analysis in parametric vector optimization problems. We prove that the proper perturbation maps and the proper efficient solution maps of parametric vector optimization problems are second-order composed proto-differentiable under some appropriate qualification conditions. Some examples are provided to illustrate our results.

scholarly journals Exploiting Block Structures of KKT Matrices for Efficient Solution of Convex Optimization Problems

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Zafar Iqbal ◽  
Saeid Nooshabadi ◽  
Ichitaro Yamazaki ◽  
Stanimire Tomov ◽  
Jack Dongarra
Keyword(s):  
Convex Optimization ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Convex Optimization Problems ◽  
Block Structures

scholarly journals Learning (from) Deep Hierarchical Structure among Features

2019 ◽  
Vol 33 ◽  
pp. 5837-5844
Author(s):  
Yu Zhang ◽  
Lei Han
Keyword(s):  
Hierarchical Structure ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Proximal Methods ◽  
Learning Tasks ◽  
Sequential Constraint ◽  
Convex Objective Function ◽  
The Hierarchical Structure ◽  
Real World Datasets ◽  
Limited Height

Data features usually can be organized in a hierarchical structure to reflect the relations among them. Most of previous studies that utilize the hierarchical structure to help improve the performance of supervised learning tasks can only handle the structure of a limited height such as 2. In this paper, we propose a Deep Hierarchical Structure (DHS) method to handle the hierarchical structure of an arbitrary height with a convex objective function. The DHS method relies on the exponents of the edge weights in the hierarchical structure but the exponents need to be given by users or set to be identical by default, which may be suboptimal. Based on the DHS method, we propose a variant to learn the exponents from data. Moreover, we consider a case where even the hierarchical structure is not available. Based on the DHS method, we propose a Learning Deep Hierarchical Structure (LDHS) method which can learn the hierarchical structure via a generalized fused-Lasso regularizer and a proposed sequential constraint. All the optimization problems are solved by proximal methods where each subproblem has an efficient solution. Experiments on synthetic and real-world datasets show the effectiveness of the proposed methods.

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