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A SEQUENTIAL QUADRATIC PROGRAMMING ALGORITHM FOR NONCONVEX, NONSMOOTH CONSTRAINED OPTIMIZATION ∗
"... Abstract. We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at points of nondifferentiability of the problem functions. We present a line search algorithm for sit ..."
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Abstract. We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at points of nondifferentiability of the problem functions. We present a line search algorithm for situations when the objective and constraint functions are locally Lipschitz and continuously differentiable on open dense subsets of R n. Our method is based on a sequential quadratic programming (SQP) algorithm that uses an ℓ1 penalty to regularize the constraints. A process of gradient sampling (GS) is employed to make the search direction computation effective in nonsmooth regions. We prove that our SQPGS method is globally convergent to stationary points with probability one and illustrate its performance with a MATLAB implementation.
BIOINFORMATICS ORIGINAL PAPER
"... doi:10.1093/bioinformatics/btl190 Independent component analysisbased penalized discriminant method for tumor classification using gene expression data ..."
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doi:10.1093/bioinformatics/btl190 Independent component analysisbased penalized discriminant method for tumor classification using gene expression data
On the Use of Piecewise Linear Models in Nonlinear Programming
, 2010
"... This paper presents an activeset algorithm for largescale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linearquadratic programming (SLQP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximati ..."
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This paper presents an activeset algorithm for largescale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linearquadratic programming (SLQP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian. 1
Acknowledgements
"... mathematical suggestions. I would also like to acknowledge the support of the Centre of Algebra at the University of Lisbon, and of ..."
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mathematical suggestions. I would also like to acknowledge the support of the Centre of Algebra at the University of Lisbon, and of
DOI 10.1007/s1107501296925 ORIGINAL PAPER
, 2011
"... A feasible SQPGS algorithm for nonconvex, nonsmooth constrained optimization ..."
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A feasible SQPGS algorithm for nonconvex, nonsmooth constrained optimization
A Sequential Quadratic . . . WITH RAPID INFEASIBILITY DETECTION
, 2012
"... We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when ..."
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We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances. A twophase strategy, carefully constructed parameter updates, and a line search are employed to promote such convergence. The first phase subproblem determines the highest level of improvement in linearized feasibility that can be attained locally. The second phase subproblem then seeks optimality in such a way that the resulting search direction attains a level of improvement in linearized feasibility that is proportional to that attained in the first phase. The subproblem formulations and parameter updates ensure that near an optimal solution, the algorithm reduces to a classical SQO method for optimization, and near an infeasible stationary point, the algorithm reduces to a (perturbed) SQO method for minimizing constraint violation. Global and local convergence guarantees for the algorithm are proved under common assumptions and numerical results are presented for a large set of test problems.
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"... An approach to improve illconditioned steepest descent methods, application to a parabolic optimal control problem via time domain decomposition. Mohamed Kamel Riahi1, CMAP, INRIASaclay and XEcole Polytechnique, Route de Saclay, 91128 Palaiseau. In this paper we present a new steepestdescent typ ..."
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An approach to improve illconditioned steepest descent methods, application to a parabolic optimal control problem via time domain decomposition. Mohamed Kamel Riahi1, CMAP, INRIASaclay and XEcole Polytechnique, Route de Saclay, 91128 Palaiseau. In this paper we present a new steepestdescent type algorithm for convex optimization problems. The method combines a Newton technique together with time domain decomposition in order to achieve the optimal steplength for the given set of descent directions. This is a parallel algorithm, where the parallel tasks turn on the control during a specific timewindow and turn it off elsewhere. This new technique significantly improves computational time compared with recognized methods. Convergence analysis of the algorithm is provided for an arbitrary choice of partition. Numerical experiments are presented to illustrate the efficiency of our algorithm.
Research on the Facilities Layout planning in MTO Manufacturing Industry Based on Genetic Algorithm
"... Abstract. To enlarge production to meet the market demand, it’s nessasery to improve the present facility layout for MTO (MakeToOrder) manufacturing enterprises. This paper tries to design a optimization method based on genetic algorithm for the facility layout of MTO enterprises. Firstly, SLP (sy ..."
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Abstract. To enlarge production to meet the market demand, it’s nessasery to improve the present facility layout for MTO (MakeToOrder) manufacturing enterprises. This paper tries to design a optimization method based on genetic algorithm for the facility layout of MTO enterprises. Firstly, SLP (systematic layout planning) was applied to analyze the material and nonmaterial flow interrelation of the workshop. Secondly, a relatively optimum layout was determined after using fuzzy hierarchy estimation to evaluate the schemes. Then the scheme was optimized with genetic algorithm. The result shows that the optimized logistics transport load is obviously less than before. This design method based on genetic algorithm (GA) is proved feasible and effective in the optimization of facility layout.