Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity
نویسندگان
چکیده
We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. make use of classical functions in an unconventional way, that only enter theoretical while algorithm itself is free. Based this idea, we are able establish several results, including first general for diminishing stepsize methods nonconvex, optimization, showing generalized stationary points, complexity study sequential quadratic programming–type algorithms.
منابع مشابه
Ghost penalties in nonconvex constrained optimization: Diminishing stepsizes and iteration complexity
We consider, for the first time, general diminishing stepsize methods for nonconvex, constrained optimization problems. We show that by using directions obtained in an SQP-like fashion convergence to generalized stationary points can be proved. In order to do so, we make use of classical penalty functions in an unconventional way. In particular, penalty functions only enter in the theoretical a...
متن کاملStructured Nonconvex and Nonsmooth Optimization: Algorithms and Iteration Complexity Analysis
Nonconvex optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology. A reason for this relatively low degree of popularity is the lack of a well developed system of theory and algorithms to support the applications, as is the case for its convex counterpart. This paper aims to take one step i...
متن کاملIteration-Complexity of a Linearized Proximal Multiblock ADMM Class for Linearly Constrained Nonconvex Optimization Problems
This paper analyzes the iteration-complexity of a class of linearized proximal multiblock alternating direction method of multipliers (ADMM) for solving linearly constrained nonconvex optimization problems. The subproblems of the linearized ADMM are obtained by partially or fully linearizing the augmented Lagrangian with respect to the corresponding minimizing block variable. The derived comple...
متن کاملOptimality and Complexity for Constrained Optimization Problems with Nonconvex Regularization
In this paper, we consider a class of constrained optimization problems where the feasible set is a general closed convex set and the objective function has a nonsmooth, nonconvex regularizer. Such regularizer includes widely used SCAD, MCP, logistic, fraction, hard thresholding and non-Lipschitz Lp penalties as special cases. Using the theory of the generalized directional derivative and the t...
متن کاملQuasi-Newton Methods for Nonconvex Constrained Multiobjective Optimization
Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2021
ISSN: ['0364-765X', '1526-5471']
DOI: https://doi.org/10.1287/moor.2020.1079