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The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in proximal-type algorithms of multiobjective optimization,…
Current state-of-the-art multi-objective optimization solvers, by computing gradients of all $m$ objective functions per iteration, produce after $k$ iterations a measure of proximity to critical conditions that is upper-bounded by…
This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in…
In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
This paper describes a study of comparison of global and one-dimensional local optimization methods to operating system scheduler tuning. The operating system scheduler we use is the Linux 2.6.23 Completely Fair Scheduler (CFS) running in…
Gradient descent (GD) is a collection of continuous optimization methods that have achieved immeasurable success in practice. Owing to data science applications, GD with diminishing step sizes has become a prominent variant. While this…
Global optimization finds applications in a wide range of real world problems. The multi-start methods are a popular class of global optimization techniques, which are based on the ideas of conducting local searches at multiple starting…
Bayesian optimization and Lipschitz optimization have developed alternative techniques for optimizing black-box functions. They each exploit a different form of prior about the function. In this work, we explore strategies to combine these…
In this paper, we introduce a novel approach to multi-modal optimization by enhancing the recently developed kinetic-based optimization (KBO) method with genetic dynamics (GKBO). The proposed method targets objective functions with multiple…
This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\"older…
In this paper, by using tools of second-order variational analysis, we study the popular forward-backward splitting method with Beck-Teboulle's line-search for solving convex optimization problem where the objective function can be split…
Local search algorithms applied to optimization problems often suffer from getting trapped in a local optimum. The common solution for this deficiency is to restart the algorithm when no progress is observed. Alternatively, one can start…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Many science and engineering applications feature non-convex optimization problems where the objective function can not be handled analytically, i.e. it is a black box. Examples include design optimization via experiments, or via costly…
We introduce LAGO, a LocAl-Global Optimization algorithm that combines gradient-enhanced Bayesian Optimization (BO) with gradient-based trust region local refinement through an adaptive competition mechanism. At each iteration, global and…
Bayesian optimization has recently emerged as a popular method for the sample-efficient optimization of expensive black-box functions. However, the application to high-dimensional problems with several thousand observations remains…
The global optimization have the very extensive applications in econometrics, science and engineering. However, the global optimization for non-convex objective functions is particularly difficult since most of the existing global…
In this paper, we present new second-order algorithms for composite convex optimization, called Contracting-domain Newton methods. These algorithms are affine-invariant and based on global second-order lower approximation for the smooth…
Gradient-based methods are widely used to solve various optimization problems, however, they are either constrained by local optima dilemmas, simple convex constraints, and continuous differentiability requirements, or limited to…