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Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…

Variational inequalities play a key role in machine learning research, such as generative adversarial networks, reinforcement learning, adversarial training, and generative models. This paper is devoted to the constrained variational…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

Many descent algorithms for multiobjective optimization have been developed in the last two decades. Tanabe et al. (Comput Optim Appl 72(2):339--361, 2019) proposed a proximal gradient method for multiobjective optimization, which can solve…

Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…

In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…

We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…

We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…

We derive efficient algorithms to compute weakly Pareto optimal solutions for smooth, convex and unconstrained multiobjective optimization problems in general Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical…

Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the…

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…

We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

Various tasks in data science are modeled utilizing the variational regularization approach, where manually selecting regularization parameters presents a challenge. The difficulty gets exacerbated when employing regularizers involving a…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…

This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange…