An Approach for Parallel Solving the Multicriterial Optimization Problems with Non-convex Constraints

2017 ◽  
pp. 121-135 ◽  
Author(s):  
Victor Gergel ◽  
Evgeny Kozinov
Keyword(s):  
Optimization Problems ◽  
Convex Constraints ◽  
Multicriterial Optimization

scholarly journals A Scaled Conjugate Gradient Method for Solving Monotone Nonlinear Equations with Convex Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Sheng Wang ◽  
Hongbo Guan
Keyword(s):  
Nonlinear Equations ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Optimization Problems ◽  
Convex Constraints ◽  
Type Method ◽  
Scaled Conjugate Gradient ◽  
Unconstrained Optimization Problems

Based on the Scaled conjugate gradient (SCALCG) method presented by Andrei (2007) and the projection method presented by Solodov and Svaiter, we propose a SCALCG method for solving monotone nonlinear equations with convex constraints. SCALCG method can be regarded as a combination of conjugate gradient method and Newton-type method for solving unconstrained optimization problems. So, it has the advantages of the both methods. It is suitable for solving large-scale problems. So, it can be applied to solving large-scale monotone nonlinear equations with convex constraints. Under reasonable conditions, we prove its global convergence. We also do some numerical experiments show that the proposed method is efficient and promising.

scholarly journals MixedH2/H∞control of flexible structures

2001 ◽  
Vol 6 (6) ◽  
pp. 557-598 ◽  
Author(s):  
D. P. De Farias ◽  
M. C. De Oliveira ◽  
J. C. Geromel
Keyword(s):  
Controller Design ◽  
Optimization Problems ◽  
Flexible Structures ◽  
Design Procedure ◽  
Theoretical Models ◽  
Convex Constraints ◽  
Feedback Controllers ◽  
Performance Function ◽  
Reduced Order ◽  
Uncertainty Models

This paper addresses the design of full order linear dynamic output feedback controllers for flexible structures. UnstructuredH∞uncertainty models are introduced for systems in modal coordinates and in reduced order form. Then a controller is designed in order to minimize a givenH2performance function while keeping the maximum supportedH∞perturbation below some appropriate level. To solve this problem we develop an algorithm able to provide local optimal solutions to optimization problems with convex constraints and non-convex but differentiable objective functions. A controller design procedure based on a trade-off curve is proposed and a simple example is solved, providing a comparison between the proposed method and the usual minimization of an upper boundH2to the norm. The method is applied to two different flexible structure theoretical models and the properties of the resulting controllers are shown in several simulations.

scholarly journals Visekriterijumska optimizacija izbora izvodjaca projekta

2003 ◽  
Vol 44 (157) ◽  
pp. 7-40
Author(s):  
Jovo Vuleta
Keyword(s):  
Optimization Problems ◽  
Optimal Solution ◽  
Real Problem ◽  
Multicriterial Optimization ◽  
Past Experiences ◽  
The Given ◽  
Mathematical Operations ◽  
Theory Of Graphs ◽  
Project Realization ◽  
Selection Of

The selection of the best (multicriterial optimal) contractors for project realization is analised in this paper. This problem is one of the most important problems that occurs during the realization of every project, especially the complex one. First we point the problem importance and past experiences and results in its solving. As a conclusion, we state that the problem of selection project realization contractors has been solved by discovering any possible solution, not necessary the optimal one. We have tried to solve one real problem using the model of integer multicriterial optimization type 0-1. The problem was presented by the appropriate mathematical model whose solving leads to multicriterial optimal solution. The special attention was paid to technique and procedure for solving the given model of integer multicriterial optimization. In order to minimize the efforts, the model has been transformed in corresponding network model whose further solving is based on the theory of graphs. The presented procedure decreases the number of mathematical operations and is more simply than most of the usual methods for solving the integer multicriterial type 0-1 optimization problems. At the end, the recommended procedure has been illustrated by a numerical example.

scholarly journals Gradient descent with non-convex constraints: local concavity determines convergence

2018 ◽  
Vol 7 (4) ◽  
pp. 755-806 ◽  
Author(s):  
Rina Foygel Barber ◽  
Wooseok Ha
Keyword(s):  
Gradient Descent ◽  
Optimization Problems ◽  
Low Rank ◽  
Convex Constraints ◽  
Geometric Properties ◽  
Projected Gradient ◽  
Matrix Estimation ◽  
Rank Estimation ◽  
Constraint Set ◽  
Projected Gradient Descent

Abstract Many problems in high-dimensional statistics and optimization involve minimization over non-convex constraints—for instance, a rank constraint for a matrix estimation problem—but little is known about the theoretical properties of such optimization problems for a general non-convex constraint set. In this paper we study the interplay between the geometric properties of the constraint set and the convergence behavior of gradient descent for minimization over this set. We develop the notion of local concavity coefficients of the constraint set, measuring the extent to which convexity is violated, which governs the behavior of projected gradient descent over this set. We demonstrate the versatility of these concavity coefficients by computing them for a range of problems in low-rank estimation, sparse estimation and other examples. Through our understanding of the role of these geometric properties in optimization, we then provide a convergence analysis when projections are calculated only approximately, leading to a more efficient method for projected gradient descent in low-rank estimation problems.

Methods for solving problems of multicriterial optimization in timber processing complex

10.12737/2184 ◽  
2014 ◽  
Vol 3 (4) ◽  
pp. 83-89
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Stochastic Algorithms ◽  
Genetic Operators ◽  
Traditional Methods ◽  
Genetic Search ◽  
Hybrid Evolutionary Algorithm ◽  
Basic Properties ◽  
Multicriterial Optimization

Basic properties of real practical optimization problems,  existence of many criteria of significant limitations, different-scale variables and algorithmic assignment of functions  make it impossible to use traditional methods. Way out of this situation is the use of adaptive stochastic algorithms, successfully overcoming these difficulties. To solve these problems it is proposed to develop a hybrid evolutionary algorithm that combines the use of the modified genetic operators (GO), selection schemes and architectures of genetic search.

scholarly journals Density of convex intersections and applications

2017 ◽  
Vol 473 (2205) ◽  
pp. 20160919 ◽  
Author(s):  
M. Hintermüller ◽  
C. N. Rautenberg ◽  
S. Rösel
Keyword(s):  
General Framework ◽  
Convex Sets ◽  
Optimization Problems ◽  
Convex Constraints ◽  
Constrained Optimization Problems ◽  
Finite Element Discretizations ◽  
Elasto Plasticity ◽  
Pointwise Constraints ◽  
Element Discretizations ◽  
Density Results

In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ -convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.

A hybrid immune–evolutionary strategy algorithm for the analysis of the wide-angle X-ray diffraction curves of semicrystalline polymers

2014 ◽  
Vol 47 (5) ◽  
pp. 1502-1511 ◽  
Author(s):  
Małgorzata Rabiej
Keyword(s):  
Reliable Method ◽  
Optimization Problems ◽  
Classical Method ◽  
Semicrystalline Polymers ◽  
Evolutionary Strategy ◽  
Wide Angle ◽  
X Ray Diffraction ◽  
X Ray ◽  
Multicriterial Optimization ◽  
Convergent Algorithm

Decomposition of wide-angle X-ray diffraction curves into crystalline peaks and amorphous components is one of the most difficult nonlinear optimization problems. For this reason, the elaboration of a reliable method that provides fast unambiguous solutions remains an important and topical task. This work presents a hybrid system dedicated to this aim, combining two methods of artificial intelligence – evolution strategies and an immune algorithm – with the classical method of Rosenbrock. A combination of the mechanisms of these three methods has given a very effective and convergent algorithm that performs very well a multicriterial optimization. Tests have shown that it is faster to converge and less ambiguous than the genetic algorithm.

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