Searching for Multiple Minima of Bound Constrained Optimization Problems using Derivative Free Optimization Techniques

2012 ◽  
Author(s):  
U.M. García Palomares
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Constrained Optimization Problems ◽  
Derivative Free Optimization ◽  
Derivative Free ◽  
Bound Constrained Optimization ◽  
Multiple Minima

scholarly journals A Derivative-Free Trust Region Algorithm with Nonmonotone Filter Technique for Bound Constrained Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Jing Gao ◽  
Jian Cao ◽  
Yueting Yang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Computational Time ◽  
Test Problems ◽  
Trust Region Algorithm ◽  
Filter Technique ◽  
Derivative Free ◽  
Bound Constrained Optimization ◽  
Parameter Values

We propose a derivative-free trust region algorithm with a nonmonotone filter technique for bound constrained optimization. The derivative-free strategy is applied for special minimization functions in which derivatives are not all available. A nonmonotone filter technique ensures not only the trust region feature but also the global convergence under reasonable assumptions. Numerical experiments demonstrate that the new algorithm is effective for bound constrained optimization. Locally, optimal parameters with respect to overall computational time on a set of test problems are identified. The performance of the best choice of parameter values obtained by the algorithm we presented which differs from traditionally used values indicates that the algorithm proposed in this paper has a certain advantage for the nondifferentiable optimization problems.

scholarly journals QGOpt: Riemannian optimization for quantum technologies

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Ilia Luchnikov ◽  
Alexander Ryzhov ◽  
Sergey Filippov ◽  
Henni Ouerdane
Keyword(s):  
Constrained Optimization ◽  
Automatic Differentiation ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Quantum Mechanical ◽  
Constrained Optimization Problems ◽  
Unitary Matrices ◽  
Riemannian Optimization ◽  
Mechanical Constraints ◽  
Quantum Technology

Many theoretical problems in quantum technology can be formulated and addressed as constrained optimization problems. The most common quantum mechanical constraints such as, e.g., orthogonality of isometric and unitary matrices, CPTP property of quantum channels, and conditions on density matrices, can be seen as quotient or embedded Riemannian manifolds. This allows to use Riemannian optimization techniques for solving quantum-mechanical constrained optimization problems. In the present work, we introduce QGOpt, the library for constrained optimization in quantum technology. QGOpt relies on the underlying Riemannian structure of quantum-mechanical constraints and permits application of standard gradient based optimization methods while preserving quantum mechanical constraints. Moreover, QGOpt is written on top of TensorFlow, which enables automatic differentiation to calculate necessary gradients for optimization. We show two application examples: quantum gate decomposition and quantum tomography.

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