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The superiorization methodology is intended to work with input data of constrained minimization problems, that is, a target function and a set of constraints. However, it is based on an antipodal way of thinking to what leads to constrained…

This study presents a novel Equiangular Direction Method (EDM) to solve a multi-objective optimization problem. We consider optimization problems, where multiple differentiable losses have to be minimized. The presented method computes…

In this paper, we illustrate a novel method for solving optimization problems when derivatives are not explicitly available. We show that combining implicit filtering (IF), an existing derivative free optimization (DFO) method, with a deep…

With the rising number of machine learning competitions, the world has witnessed an exciting race for the best algorithms. However, the involved data selection process may fundamentally suffer from evidence ambiguity and concept drift…

During the training of networks for distance metric learning, minimizers of the typical loss functions can be considered as "feasible points" satisfying a set of constraints imposed by the training data. To this end, we reformulate distance…

We present a simple and at the same time fficient algorithm to compute all nondominated extreme points in the outcome set of multi-objective mixed integer linear programmes in any dimension. The method generalizes the well-known dichotomic…

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…

Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…

The streaming max-min diversification problem concerns the selection of a limited and diverse sample of items out of a data stream of known finite length. The objective to be maximized is the minimum distance among any pair of selected…

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational…

In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the…

Decision diagrams (DDs) have emerged as a state-of-the-art method for exact multiobjective integer linear programming. When the DD is too large to fit into memory or the decision-maker prefers a fast approximation to the Pareto frontier,…

Recent studies show LLMs struggle with complex instructions involving multiple constraints (e.g., length, format, sentiment). Existing works address this issue by fine-tuning, which heavily relies on fine-tuning data quality and is…

A class of interior point methods using inexact directions is analysed. The linear system arising in interior point methods for linear programming is reformulated such that the solution is less sensitive to perturbations in the right-hand…

Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…

Real-world data such as digital images, MRI scans and electroencephalography signals are naturally represented as matrices with structural information. Most existing classifiers aim to capture these structures by regularizing the regression…

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…

Practical applications of mechanical metamaterials often involve solving inverse problems where the objective is to find the (multiple) microarchitectures that give rise to a given set of properties. The limited resolution of additive…

Although the performance of popular optimization algorithms such as Douglas-Rachford splitting (DRS) and the ADMM is satisfactory in small and well-scaled problems, ill conditioning and problem size pose a severe obstacle to their reliable…

The use of deep learning methods for solving PDEs is a field in full expansion. In particular, Physical Informed Neural Networks, that implement a sampling of the physical domain and use a loss function that penalizes the violation of the…