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Weakly Quasar-Convex Optimization
Abbas Khademi, Felipe Lara
This paper introduces the class of weakly quasar-convex functions, a notion that simultaneously generalizes weak convexity (and hence convexity) and quasar-convexity. We establish…
Robust Learning Meets Quasar-Convex Optimization: Inexact High-Order Proximal-Point Methods
Alireza Kabgani, Felipe Lara, Masoud Ahookhosh
Robust learning aims to maintain model performance under noise, corruption, and distributional shifts, which are prevalent in modern machine learning applications. This work shows…
Quasar-Convex Optimization: Fundamental Properties and High-Order Proximal-Point Methods
Masoud Ahookhosh, Jose M. M. de Brito, Alireza Kabgani +2
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable propertie…
Discontinuous Strongly Quasiconvex Functions
Nguyen Thi Van Hang, Felipe Lara, Nguyen Dong Yen
A fundamental open question asking whether all real-valued strongly quasiconvex functions defined on are necessarily continuous, akin to their convex counterparts, is…
Characterizations of Strongly Quasiconvex Functions
Nicolas Hadjisavvas, Felipe Lara
We provide new necessary and sufficient conditons for ensuring strong quasiconvexity in the nonsmooth case and, as a consequence, we provide a proof for the differentiable case. Fu…
Extending Linear Convergence of the Proximal Point Algorithm: The Quasar-Convex Case
José de Brito, Felipe Lara, Di Liu
This work investigates the properties of the proximity operator for quasar-convex functions and establishes the convergence of the proximal point algorithm to a global minimizer wi…
Asymptotic Convergence Analysis of High-Order Proximal-Point Methods Beyond Sublinear Rates
Masoud Ahookhosh, Alfredo Iusem, Alireza Kabgani +1
This paper investigates the asymptotic convergence behavior of the high-order proximal-point algorithm (HiPPA) to global minimizers, extending existing analyses beyond sublinear co…
Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications
Felipe Lara, Cristian Vega
We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular,…
Strongly quasiconvex functions: what we know (so far)
Sorin-Mihai Grad, Felipe Lara, Raúl T. Marcavillaca
Introduced by Polyak in 1966, the class of strongly quasiconvex functions includes some interesting nonconvex members, like the square root of the Euclidean norm or ratios with a n…
Weak sharp minima at infinity and solution stability in mathematical programming via asymptotic analysis
Felipe Lara, Nguyen Van Tuyen, Tran Van Nghi
We develop sufficient conditions for the existence of the weak sharp minima at infinity property for nonsmooth optimization problems via asymptotic cones and generalized asymptotic…
Characterizations, Dynamical Systems and Gradient Methods for Strongly Quasiconvex Functions
Felipe Lara, Raúl T. Marcavillaca, Phan T. Vuong
We study differentiable strongly quasiconvex functions for providing new properties for algorithmic and monotonicity purposes. Furthemore, we provide insights into the decreasing b…