scholarly journals A Continuation Method for the Efficient Solution of Parametric Optimization Problems in Kinetic Model Reduction

2013 ◽  
Vol 35 (3) ◽  
pp. A1584-A1603 ◽  
Author(s):  
Dirk Lebiedz ◽  
Jochen Siehr
Keyword(s):  
Kinetic Model ◽  
Model Reduction ◽  
Efficient Solution ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Continuation Method

scholarly journals A certified RB method for PDE-constrained parametric optimization problems

2019 ◽  
Vol 10 (1) ◽  
pp. 123-152
Author(s):  
Andrea Manzoni ◽  
Stefano Pagani
Keyword(s):  
Optimal Control ◽  
Efficient Solution ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
A Posteriori Error Estimates ◽  
Optimal Solution ◽  
Posteriori Error ◽  
Elliptic Pdes ◽  
Reduced Basis ◽  
Cost Functionals

Abstract We present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameter vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, the cost functional, its gradient and the optimal solution. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows.

scholarly journals R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

2021 ◽  
Author(s):  
Patrick Mehlitz ◽  
Leonid I. Minchenko
Keyword(s):  
Linear Dependence ◽  
Constraint Qualification ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Bilevel Optimization ◽  
Regularity Property ◽  
Constant Rank Constraint Qualification ◽  
Existence Criterion ◽  
Set Valued Mappings

AbstractThe presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

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.

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