A filter-variable-metric method for nonsmooth convex constrained optimization

Peng, Yehui; Feng, Heying; Li, Qiyong

doi:10.1016/j.amc.2008.11.019

Cited by 7 publications

(4 citation statements)

References 17 publications

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“…Filter methods (see [12] and references therein, and-for the nondifferentiable case- [18,34]) employ feasibility restoration steps to reduce the value of a constraint violation function. In [4] dynamical steering of exact penalty methods toward feasibility and optimality is reviewed and analysed.…”

Section: Outline and Main Resultsmentioning

confidence: 99%

Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems

et al. 2016

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Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? We answer this question in the affirmative for a convex program and an associated subgradient algorithm for its Lagrange dual. We show that the primal-dual pair of programs corresponding to an associated homogeneous dual function is in turn associated with a saddle-point problem, in which-in the inconsistent case-the primal part amounts to finding a solution in the primal space such that the Euclidean norm of the infeasibility in the relaxed constraints is minimized; the dual part amounts to identifying a feasible steepest ascent direction for the Lagrangian dual function. We present convergence results for a conditional ε-subgradient optimization algorithm applied to the Lagrangian dual problem, and the construction of an ergodic sequence of primal subproblem solutions; this composite algorithm yields convergence of the primal-dual sequence to the set of saddle-points of the associated homogeneous Lagrangian function; for linear programs, convergence to the subset in which the primal objective is at minimum is also achieved. Keywords Mathematics Subject Classification

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Section: Outline and Main Resultsmentioning

confidence: 99%

Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems

et al. 2016

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“…As mentioned above, the determination of the descent direction v k usually involves the gradient g k = ∇f (x k ) of the objective function at the point x k , which may be not defined due to the lack of regularity of f (Peng and Heying, 2009;Uryasev, 1991). In addition, the objective function is not assumed to be convex and its subdifferential may be empty.…”

Section: Projected Variable Metric Methodsmentioning

confidence: 99%

Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

Mouatasim¹,

Ellaia²,

Cursi³

2011

International Journal of Applied Mathematics and Computer Science

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We present a random perturbation of the projected variable metric method for solving linearly constrained nonsmooth (i.e., nondifferentiable) nonconvex optimization problems, and we establish the convergence to a global minimum for a locally Lipschitz continuous objective function which may be nondifferentiable on a countable set of points. Numerical results show the effectiveness of the proposed approach.

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“…Filter methods have been combined with trust-region approaches [2,3], SQP techniques [4,5], inexact restoration algorithms [6,7], interior point strategies [8] and line-search algorithms [9,10,11]. They also have been extended to other areas of optimization such as nonlinear equations and inequalities [12,13,14,15], nonsmooth optimization [16,17], unconstrained optimization [18,19], complementarity problems [20,21] and derivativefree optimization [22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

Macêdo

Costa

Rocha

et al. 2017

Lecture Notes in Computer Science

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In this work we present an algorithm that combines the filter technique and the dynamically dimensioned search (DDS) for solving nonlinear and nonconvex constrained global optimization problems. The DDS is a stochastic global algorithm for solving bound constrained problems that in each iteration generates a randomly trial point perturbing some coordinates of the current best point. The filter technique controls the progress related to optimality and feasibility defining a forbidden region of points refused by the algorithm. This region can be given by the flat or slanting filter rule. The proposed algorithm does not compute or approximate any derivatives of the objective and constraint functions. Preliminary experiments show that the proposed algorithm gives competitive results when compared with other methods.

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A filter-variable-metric method for nonsmooth convex constrained optimization

Cited by 7 publications

References 17 publications

Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems

Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems

Random perturbation of the projected variable metric method for nonsmooth nonconvex optimization problems with linear constraints

Combining Filter Method and Dynamically Dimensioned Search for Constrained Global Optimization

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