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We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
Numerous real-world applications of uncertain multiobjective optimization problems (UMOPs) can be found in science, engineering, business, and management. To handle the solution of uncertain optimization problems, robust optimization is a…
Prior work in multi-objective reinforcement learning typically uses linear reward scalarization with fixed weights, which provably fails to capture non-convex Pareto fronts and thus yields suboptimal results. This limitation becomes…
This paper is devoted to the investigation of inertial dynamical systems with implicit Hessian-driven damping for strongly quasiconvex optimization which is a specific class of nonconvex optimization problems. We first establish exponential…
In this article we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since…
We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By…
In this paper, we investigate the multi-objective optimal control problem of ordinary differential equations on Riemannian manifolds. We first obtain the second-order necessary conditions for weak Pareto optimal solutions for…
Multi-objective optimization aims at finding trade-off solutions to conflicting objectives. These constitute the Pareto optimal set. In the context of expensive-to-evaluate functions, it is impossible and often non-informative to look for…
Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…
In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…
This paper generalizes the dynamical system proposed by Wang et al. [Siam. J. Sci. Comput., 2021] to multiobjective optimization by investigating a multiobjective accelerated gradient-like flow with asymptotically vanishing normalized…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…
We introduce a new dynamical system, at the interface between second-order dynamics with inertia and Newton's method. This system extends the class of inertial Newton-like dynamics by featuring a time-dependent parameter in front of the…
In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box.…
Randomly initialized first-order optimization algorithms are the method of choice for solving many high-dimensional nonconvex problems in machine learning, yet general theoretical guarantees cannot rule out convergence to critical points of…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse…