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A proximal method for composite minimization
, 2008
"... Abstract. We consider minimization of functions that are compositions of proxregular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a r ..."
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Cited by 8 (2 self)
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Abstract. We consider minimization of functions that are compositions of proxregular functions with smooth vector functions. A wide variety of important optimization problems can be formulated in this way. We describe a subproblem constructed from a linearized approximation to the objective and a regularization term, investigating the properties of local solutions of this subproblem and showing that they eventually identify a manifold containing the solution of the original problem. We propose an algorithmic framework based on this subproblem and prove a global convergence result.
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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Cited by 1 (0 self)
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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
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.