scholarly journals A parameter-free unconstrained reformulation for nonsmooth problems with convex constraints

2021 ◽  
Author(s):  
Giulio Galvan ◽  
Marco Sciandrone ◽  
Stefano Lucidi
Keyword(s):  
Optimization Methods ◽  
Local Minima ◽  
Convex Constraints ◽  
Nonsmooth Problems ◽  
Constrained Problem ◽  
Nonsmooth Problem ◽  
Feasible Sets ◽  
Unconstrained Problem ◽  
Global And Local ◽  
State Of Art

AbstractIn the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard nonsmooth optimization methods if we are able to make projections onto the feasible sets. Numerical evidence shows that the proposed formulation compares favorably against state-of-art approaches. Code can be found at https://github.com/jth3galv/dfppm.

scholarly journals On critical points of quadratic low-rank matrix optimization problems

2020 ◽  
Vol 40 (4) ◽  
pp. 2626-2651
Author(s):  
André Uschmajew ◽  
Bart Vandereycken
Keyword(s):  
Critical Points ◽  
Optimization Problems ◽  
Quadratic Function ◽  
Singular Values ◽  
Positive Semidefinite ◽  
Optimization Methods ◽  
Low Rank ◽  
Local Minima ◽  
Rank Matrix ◽  
Low Rank Matrix

Abstract The absence of spurious local minima in certain nonconvex low-rank matrix recovery problems has been of recent interest in computer science, machine learning and compressed sensing since it explains the convergence of some low-rank optimization methods to global optima. One such example is low-rank matrix sensing under restricted isometry properties (RIPs). It can be formulated as a minimization problem for a quadratic function on the Riemannian manifold of low-rank matrices, with a positive semidefinite Riemannian Hessian that acts almost like an identity on low-rank matrices. In this work new estimates for singular values of local minima for such problems are given, which lead to improved bounds on RIP constants to ensure absence of nonoptimal local minima and sufficiently negative curvature at all other critical points. A geometric viewpoint is taken, which is inspired by the fact that the Euclidean distance function to a rank-$k$ matrix possesses no critical points on the corresponding embedded submanifold of rank-$k$ matrices except for the single global minimum.

Torsion Angle Refinement and Dynamics as a Tool to Aid Crystallographic Structure Determination

2009 ◽  
Author(s):  
Ralf W. Grosse-Kunstleve ◽  
Nigel W. Moriarty ◽  
Paul D. Adams
Keyword(s):  
Torsion Angle ◽  
Data Bank ◽  
Optimization Methods ◽  
Rigid Body Dynamics ◽  
Optimization Techniques ◽  
Conformational Space ◽  
Crystallographic Structure ◽  
Local Minima ◽  
Body Dynamics ◽  
Angle Space

Crystallographic methods using experimental diffraction data have produced about 85% of the macromolecular structures in the Protein Data Bank. Before deposition, nearly all crystal structures are refined with gradient-driven optimization techniques. Refinement is typically performed with iterative local optimization methods. A common problem is convergence to local minima. Reparameterization of the model in torsion angle space reduces the number of parameters. This in itself can help to escape from local minima. Combination with rigid-body dynamics algorithms results in an important tool for sampling conformational space. This paper presents the torsion angle refinement and dynamics algorithms implemented for the phenix.refine program and the results of various tests.

Global and local minima of protonated acetonitrile clusters

2020 ◽  
Vol 44 (40) ◽  
pp. 17558-17569 ◽  
Author(s):  
Alhadji Malloum ◽  
Jeanet Conradie
Keyword(s):  
Hydrogen Bonds ◽  
Potential Energy ◽  
Potential Energy Surfaces ◽  
Local Minima ◽  
Energy Surfaces ◽  
Global And Local

Potential energy surfaces of protonated acetonitrile clusters have been explored to locate global and local minima energy structures. The structures are stabilized by strong hydrogen bonds, anti-parallel dimers, dipole–dipole and CH⋯N interactions.

scholarly journals AUV-Method for a Class of Constrained Minimized Problems of Maximum Eigenvalue Functions

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Wei Wang ◽  
Ming Jin ◽  
Shanghua Li ◽  
Xinyu Cao
Keyword(s):  
Exact Penalty ◽  
Maximum Eigenvalue ◽  
Convex Approximation ◽  
Equivalent Problem ◽  
Composite Function ◽  
Primal Problem ◽  
Approximate Problem ◽  
Constrained Problem ◽  
Constrained Minimization Problem ◽  
Unconstrained Problem

In this paper, we apply theUV-algorithm to solve the constrained minimization problem of a maximum eigenvalue function which is the composite function of an affine matrix-valued mapping and its maximum eigenvalue. Here, we convert the constrained problem into its equivalent unconstrained problem by the exact penalty function. However, the equivalent problem involves the sum of two nonsmooth functions, which makes it difficult to applyUV-algorithm to get the solution of the problem. Hence, our strategy first applies the smooth convex approximation of maximum eigenvalue function to get the approximate problem of the equivalent problem. Then the approximate problem, the space decomposition, and theU-Lagrangian of the object function at a given point will be addressed particularly. Finally, theUV-algorithm will be presented to get the approximate solution of the primal problem by solving the approximate problem.

State of art of optimization methods for assembly line design

2002 ◽  
Vol 26 (2) ◽  
pp. 163-174 ◽  
Author(s):  
Brahim Rekiek ◽  
Alexandre Dolgui ◽  
Alain Delchambre ◽  
Antoneta Bratcu
Keyword(s):  
Assembly Line ◽  
Optimization Methods ◽  
Line Design ◽  
State Of Art

scholarly journals APPLICATION OF GLOBAL OPTIMIZATION TO PREDICT STRAINS IN RC COMPRESSED COLUMNS

2021 ◽  
Vol 61 (1) ◽  
pp. 242-252
Author(s):  
Marek Lechman ◽  
Andrzej Stachurski
Keyword(s):  
Least Squares Method ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Trust Region ◽  
Global Solutions ◽  
Optimization Methods ◽  
Box Constraints ◽  
Particle Swarm Method ◽  
Global And Local Optimization ◽  
Global And Local

In this paper, the results of an application of global and local optimization methods to solve a problem of determination of strains in RC compressed structure members are presented. Solutions of appropriate sets of nonlinear equations in the presence of box constraints have to be found. The use of the least squares method leads to finding global solutions of optimization problems with box constraints. Numerical examples illustrate the effects of the loading value and the loading eccentricity on the strains in concrete and reinforcing steel in the a cross-section.Three different minimization methods were applied to compute them: trust region reflective, genetic algorithm tailored to problems with real double variables and particle swarm method. Numerical results on practical data are presented. In some cases, several solutions were found. Their existence has been detected by the local search with multistart, while the genetic and particle swarm methods failed to recognize their presence.

Global and Local Surrogate-Model-Assisted Differential Evolution for Waterflooding Production Optimization

SPE Journal ◽  
2019 ◽  
Vol 25 (01) ◽  
pp. 105-118 ◽  
Author(s):  
Guodong Chen ◽  
Kai Zhang ◽  
Liming Zhang ◽  
Xiaoming Xue ◽  
Dezhuang Ji ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Surrogate Model ◽  
Net Present Value ◽  
Channel Model ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Production Optimization ◽  
Optimization Process ◽  
Promising Area ◽  
Global And Local

Summary Surrogate models, which have become a popular approach to oil-reservoir production-optimization problems, use a computationally inexpensive approximation function to replace the computationally expensive objective function computed by a numerical simulator. In this paper, a new optimization algorithm called global and local surrogate-model-assisted differential evolution (GLSADE) is introduced for waterflooding production-optimization problems. The proposed method consists of two parts: (1) a global surrogate-model-assisted differential-evolution (DE) part, in which DE is used to generate multiple offspring, and (2) a local surrogate-model-assisted DE part, in which DE is used to search for the optimum of the surrogate. The cooperation between global optimization and local search helps the production-optimization process become more efficient and more effective. Compared with the conventional one-shot surrogate-based approach, the developed method iteratively selects data points to enhance the accuracy of the promising area of the surrogate model, which can substantially improve the optimization process. To the best of our knowledge, the proposed method uses a state-of-the-art surrogate framework for production-optimization problems. The approach is tested on two 100-dimensional benchmark functions, a three-channel model, and the egg model. The results show that the proposed method can achieve higher net present value (NPV) and better convergence speed in comparison with the traditional evolutionary algorithm and other surrogate-assisted optimization methods for production-optimization problems.

scholarly journals Harmonic Elimination of Cascaded Multilevel Inverter using Metaheuristic Optimization Methods

2018 ◽  
Vol 7 (4.15) ◽  
pp. 272 ◽  
Author(s):  
Srikanta Kumar Dash ◽  
Byamakesh Nayak ◽  
Jiban Ballav Sahu ◽  
Rojalin Rout
Keyword(s):  
Harmonic Distortion ◽  
Optimization Methods ◽  
Optimization Method ◽  
Multilevel Inverter ◽  
Computational Time ◽  
Local Minima ◽  
Metaheuristic Optimization ◽  
Harmonic Elimination ◽  
Whale Optimization ◽  
Cascaded Multilevel Inverter

The harmonic elimination of multilevel inverters is a complicated task that includes nonlinear transcendental equations. With the increase in the level of the multilevel inverter, the no of variables of the equation also increases which makes the problem more complicated. Metaheuristic optimization algorithms play an important role in finding out optimum switching angles required for elimination of harmonics in a lesser computational time avoiding multiple local minima. This paper deals with the harmonic elimination of cascaded multilevel inverter using whale optimization algorithm. The whale optimization method has the ability to escape local minima and it takes less time of computation of results. Results are verified theoretically by taking an example of a 15-level cascaded H-bridge inverter fed from equal d.c.sources. The above scheme well minimizes lower order harmonics and gives better output voltage and a low total harmonic distortion.  

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