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Inexact Reduced Gradient Methods in Nonconvex Optimization
This paper proposes and develops new linesearch methods with inexact gradient information for finding stationary points of nonconvex continuously...
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Low-rank matrix estimation via nonconvex optimization methods in multi-response errors-in-variables regression
Noisy and missing data cannot be avoided in real application, such as bioinformatics, economics and remote sensing. Existing methods mainly focus on...
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Newton and interior-point methods for (constrained) nonconvex–nonconcave minmax optimization with stability and instability guarantees
We address the problem of finding a local solution to a nonconvex–nonconcave minmax optimization using Newton type methods, including primal-dual...
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Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition
Many tasks in real life scenarios can be naturally formulated as nonconvex optimization problems. Unfortunately, to date, the iterative numerical...
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The Nonconvex Second-Order Cone: Algebraic Structure Toward Optimization
This paper explores the nonconvex second-order cone as a nonconvex conic extension of the known convex second-order cone in optimization, as well as...
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A Solver for Multiobjective Mixed-Integer Convex and Nonconvex Optimization
This paper proposes a general framework for solving multiobjective nonconvex optimization problems, i.e., optimization problems in which multiple...
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Generalized Derivatives and Optimality Conditions in Nonconvex Optimization
In this paper, we study the radial epiderivative notion for nonconvex functions, which extends the (classical) directional derivative concept. The...
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Three Search Algorithms for Three Nonconvex Optimization Problems
The paper deals with three numerical approaches that allow one to construct computational technologies for solving nonconvex optimization problems....
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A Hybrid and Inexact Algorithm for Nonconvex and Nonsmooth Optimization
The problem of nonconvex and nonsmooth optimization (NNO) has been extensively studied in the machine learning community, leading to the development...
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A class of infeasible proximal bundle methods for nonsmooth nonconvex multi-objective optimization problems
We propose a class of infeasible proximal bundle methods for solving nonsmooth nonconvex multi-objective optimization problems. The proposed...
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Frank–Wolfe-type methods for a class of nonconvex inequality-constrained problems
The Frank–Wolfe (FW) method, which implements efficient linear oracles that minimize linear approximations of the objective function over a fixed ...
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A Bregman-style Partially Symmetric Alternating Direction Method of Multipliers for Nonconvex Multi-block Optimization
The alternating direction method of multipliers (ADMM) is one of the most successful and powerful methods for separable minimization optimization....
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Nonsmooth nonconvex optimization on Riemannian manifolds via bundle trust region algorithm
This paper develops an iterative algorithm to solve nonsmooth nonconvex optimization problems on complete Riemannian manifolds. The algorithm is...
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Optimization over the Pareto front of nonconvex multi-objective optimal control problems
Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best...
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Stochastic first-order methods for convex and nonconvex functional constrained optimization
Functional constrained optimization is becoming more and more important in machine learning and operations research. Such problems have potential...
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An Adaptive Superfast Inexact Proximal Augmented Lagrangian Method for Smooth Nonconvex Composite Optimization Problems
This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite...
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A two-level distributed algorithm for nonconvex constrained optimization
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The...
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Nonconvex and Nonsmooth Sparse Optimization via Adaptively Iterative Reweighted Methods
We propose a general formulation of nonconvex and nonsmooth sparse optimization problems with convex set constraint, which can take into account most...
