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In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
The trend in modern science and technology is to take vector measurements rather than scalars, ruthlessly scaling to ever higher dimensional vectors. For about two decades now, traditional scalar Compressed Sensing has been synonymous with…
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from…
In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild assumptions, we provide global rate of convergence of these…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
In prioritization schemes, based on pairwise comparisons, such as the Analytical Hierarchy Process, it is important to extract a cardinal ranking vector from a reciprocal matrix that is unlikely to be consistent. It is natural to choose…
In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
We study black-box vector optimization with Gaussian process bandits, where there is an incomplete order relation on objective vectors described by a polyhedral convex cone. Existing black-box vector optimization approaches either suffer…
Time-varying non-convex continuous-valued non-linear constrained optimization is a fundamental problem. We study conditions wherein a momentum-like regularising term allow for the tracking of local optima by considering an ordinary…
When considering an unconstrained minimization problem, a standard approach is to solve the optimality system with a Newton method possibly preconditioned by, e.g., nonlinear elimination. In this contribution, we argue that nonlinear…