Related papers: Inexact Proximal Newton methods in Hilbert spaces
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
We use the concept of barrier-based smoothing approximations introduced in [ C. B. Chua and Z. Li, A barrier-based smoothing proximal point algorithm for NCPs over closed convex cones, SIOPT 23(2), 2010] to extend the non-interior…
Successive quadratic approximations (SQA) are numerically efficient for minimizing the sum of a smooth function and a convex function. The iteration complexity of inexact SQA methods has been analyzed recently. In this paper, we present an…
Gradient-based algorithms are one of the methods of choice for the optimisation of Markov Decision Processes. In this article we will present a novel approximate Newton algorithm for the optimisation of such models. The algorithm has…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…
We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Optimization plays a key role in machine learning. Recently, stochastic second-order methods have attracted much attention due to their low computational cost in each iteration. However, these algorithms might perform poorly especially if…
In this paper, inexact Gauss-Newton like methods for solving injective-overdetermined systems of equations are studied. We use a majorant condition, defined by a function whose derivative is not necessarily convex, to extend and improve…
In this paper, we propose a novel primal-dual inexact gradient projection method for nonlinear optimization problems with convex-set constraint. This method only needs inexact computation of the projections onto the convex set for each…
In this paper, we present a local convergence analysis of inexact Gauss-Newton like methods for solving nonlinear least squares problems. Under the hypothesis that the derivative of the function associated with the least square problem…
This paper considers the problem of minimizing the summation of a differentiable function and a nonsmooth function on a Riemannian manifold. In recent years, proximal gradient method and its invariants have been generalized to the…
We present two quantum interior point methods for semidefinite optimization problems, building on recent advances in quantum linear system algorithms. The first scheme, more similar to a classical solution algorithm, computes an inexact…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton's method for self-concordant functions, including the case of inexact search…
Conformance checking techniques let us find out to what degree a process model and real execution data correspond to each other. In recent years, alignments have proven extremely useful in calculating conformance statistics. Most techniques…
Most models in machine learning contain at least one hyperparameter to control for model complexity. Choosing an appropriate set of hyperparameters is both crucial in terms of model accuracy and computationally challenging. In this work we…
Historically speaking, it is hard to balance the global and local efficiency of second-order optimization algorithms. For instance, the classical Newton's method possesses excellent local convergence but lacks global guarantees, often…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function via the inexact accelerated proximal gradient (APG) method. A key limitation of existing inexact APG methods is their reliance on…