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The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal…

This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and H\"older continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It…

We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…

Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…

We present a derivative-based algorithm for nonlinearly constrained optimization problems that is tolerant of inaccuracies in the data. The algorithm solves a semi-smooth set of nonlinear equations that are equivalent to the first-order…

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…

Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…

We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…

In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…

The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…

Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…

An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…

Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…

The combinatorial optimization problem is one of the important applications in neural network computation. The solutions of linearly constrained continuous optimization problems are difficult with an exact algorithm, but the algorithm for…

Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…

In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…