scholarly journals Invariant Geometric Curvilinear Optimization with Restricted Evolution Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 802
Author(s):  
Andreea Bejenaru
Keyword(s):  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimization Problems ◽  
Constraint Optimization ◽  
Single Time ◽  
Evolution Dynamics ◽  
Constraint Optimization Problems ◽  
The Cost ◽  
Cost Functionals ◽  
Inequality Type

This paper begins with a geometric statement of constraint optimization problems, which include both equality and inequality-type restrictions. The cost to optimize is a curvilinear functional defined by a given differential one-form, while the optimal state to be determined is a differential curve connecting two given points, among all the curves satisfying some given primal feasibility conditions. The resulting outcome is an invariant curvilinear Fritz–John maximum principle. Afterward, this result is approached by means of parametric equations. The classical single-time Pontryagin maximum principle for curvilinear cost functionals is revealed as a consequence.

Algorithm for Distributed Constraint Optimization Problems with Low Constraint Density

2011 ◽  
Vol 22 (4) ◽  
pp. 625-639 ◽  
Author(s):  
Bo DING ◽  
Huai-Min WANG ◽  
Dian-Xi SHI ◽  
Yang-Bin TANG
Keyword(s):  
Optimization Problems ◽  
Constraint Optimization ◽  
Distributed Constraint Optimization ◽  
Low Constraint ◽  
Constraint Optimization Problems

Applying Max-sum to asymmetric distributed constraint optimization problems

2020 ◽  
Vol 34 (1) ◽  
Author(s):  
Roie Zivan ◽  
Tomer Parash ◽  
Liel Cohen-Lavi ◽  
Yarden Naveh
Keyword(s):  
Optimization Problems ◽  
Constraint Optimization ◽  
Distributed Constraint Optimization ◽  
Constraint Optimization Problems

scholarly journals Beyond Trees: Analysis and Convergence of Belief Propagation in Graphs with Multiple Cycles

2020 ◽  
Vol 34 (05) ◽  
pp. 7333-7340
Author(s):  
Roie Zivan ◽  
Omer Lev ◽  
Rotem Galiki
Keyword(s):  
Graphical Models ◽  
Belief Propagation ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Damping Factor ◽  
Constraint Optimization ◽  
Single Cycle ◽  
Distributed Constraint Optimization ◽  
Multiple Cycles ◽  
Constraint Optimization Problems

Belief propagation, an algorithm for solving problems represented by graphical models, has long been known to converge to the optimal solution when the graph is a tree. When the graph representing the problem includes a single cycle, the algorithm either converges to the optimal solution or performs periodic oscillations. While the conditions that trigger these two behaviors have been established, the question regarding the convergence and divergence of the algorithm on graphs that include more than one cycle is still open.Focusing on Max-sum, the version of belief propagation for solving distributed constraint optimization problems (DCOPs), we extend the theory on the behavior of belief propagation in general – and Max-sum specifically – when solving problems represented by graphs with multiple cycles. This includes: 1) Generalizing the results obtained for graphs with a single cycle to graphs with multiple cycles, by using backtrack cost trees (BCT). 2) Proving that when the algorithm is applied to adjacent symmetric cycles, the use of a large enough damping factor guarantees convergence to the optimal solution.

scholarly journals Multi-Context System for Optimization Problems

2019 ◽  
Vol 33 ◽  
pp. 2929-2937
Author(s):  
Tiep Le ◽  
Tran Cao Son ◽  
Enrico Pontelli
Keyword(s):  
Complexity Analysis ◽  
Optimization Problems ◽  
Distributed Optimization ◽  
Multi Agent System ◽  
Constraint Optimization ◽  
Agent System ◽  
Distributed Constraint Optimization ◽  
Multi Agent ◽  
Definition Of ◽  
Constraint Optimization Problems

This paper proposes Multi-context System for Optimization Problems (MCS-OP) by introducing conditional costassignment bridge rules to Multi-context Systems (MCS). This novel feature facilitates the definition of a preorder among equilibria, based on the total incurred cost of applied bridge rules. As an application of MCS-OP, the paper describes how MCS-OP can be used in modeling Distributed Constraint Optimization Problems (DCOP), a prominent class of distributed optimization problems that is frequently employed in multi-agent system (MAS) research. The paper shows, by means of an example, that MCS-OP is more expressive than DCOP, and hence, could potentially be useful in modeling distributed optimization problems which cannot be easily dealt with using DCOPs. It also contains a complexity analysis of MCS-OP.

scholarly journals A Particle Swarm Based Algorithm for Functional Distributed Constraint Optimization Problems

2020 ◽  
Vol 34 (05) ◽  
pp. 7111-7118
Author(s):  
Moumita Choudhury ◽  
Saaduddin Mahmud ◽  
Md. Mosaddek Khan
Keyword(s):  
Optimization Problems ◽  
State Of The Art ◽  
Particle Swarm ◽  
Continuous Optimization ◽  
Continuous Variables ◽  
Constraint Optimization ◽  
Solution Quality ◽  
Distributed Constraint Optimization ◽  
Continuous Optimization Problems ◽  
Constraint Optimization Problems

Distributed Constraint Optimization Problems (DCOPs) are a widely studied constraint handling framework. The objective of a DCOP algorithm is to optimize a global objective function that can be described as the aggregation of several distributed constraint cost functions. In a DCOP, each of these functions is defined by a set of discrete variables. However, in many applications, such as target tracking or sleep scheduling in sensor networks, continuous valued variables are more suited than the discrete ones. Considering this, Functional DCOPs (F-DCOPs) have been proposed that can explicitly model a problem containing continuous variables. Nevertheless, state-of-the-art F-DCOPs approaches experience onerous memory or computation overhead. To address this issue, we propose a new F-DCOP algorithm, namely Particle Swarm based F-DCOP (PFD), which is inspired by a meta-heuristic, Particle Swarm Optimization (PSO). Although it has been successfully applied to many continuous optimization problems, the potential of PSO has not been utilized in F-DCOPs. To be exact, PFD devises a distributed method of solution construction while significantly reducing the computation and memory requirements. Moreover, we theoretically prove that PFD is an anytime algorithm. Finally, our empirical results indicate that PFD outperforms the state-of-the-art approaches in terms of solution quality and computation overhead.

scholarly journals Portfolio approaches for constraint optimization problems

2015 ◽  
Vol 76 (1-2) ◽  
pp. 229-246 ◽  
Author(s):  
Roberto Amadini ◽  
Maurizio Gabbrielli ◽  
Jacopo Mauro
Keyword(s):  
Optimization Problems ◽  
Constraint Optimization ◽  
Constraint Optimization Problems
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