arXiv subjects

Monika Syga

Publications and source records attributed to Monika Syga.

9 recordsLinked to original sources

arXiv2026

On the application of the Wasserstein metric to 2D curves classification

In this work we analyse a number of variants of the Wasserstein distance which allow to focus the classification on the prescribed parts (fragments) of classified 2D curves. These variants are based on the use of a number of discrete probability measures which reflect the importance of given fragments of curves. The performance of this approach is tested through a series of experiments related to the clustering analysis of 2D curves performed on data coming from the field of archaeology.

cs.CV↗

arXiv2024

Primal-dual algorithm for weakly convex functions under sharpness conditions

We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap function. Under the sharpness condition of this new function, we identify the area around the set of saddle points where we obtain the convergence of the primal-dual algorithm. We give numerical examples and applications in image denoising and deblurring to demonstrate our results.

math.OC↗

arXiv2024

Characterisation of zero duality gap for optimization problems in spaces without linear structure

We prove sufficient and necessary conditions ensuring zero duality gap for Lagrangian duality in some classes of nonconvex optimization problems. To this aim, we use the $\Phi$-convexity theory and minimax theorems for $\Phi$-convex functions. The obtained zero duality results apply to optimization problems involving prox-bounded functions, DC functions, weakly convex functions and paraconvex functions as well as infinite-dimensional linear optimization problems, including Kantorovich duality which plays an important role in determining Wasserstein distance.

math.OC↗

arXiv2021

A comprehensive study of clustering a class of 2D shapes

The paper concerns clustering with respect to the shape and size of 2D contours that are boundaries of cross-sections of 3D objects of revolution. We propose a number of similarity measures based on combined disparate Procrustes analysis (PA) and Dynamic Time Warping (DTW) distances. Motivation and the main application for this study comes from archaeology. The performed computational experiments refer to the clustering of archaeological pottery.

cs.CV↗

arXiv2021

On duality for nonconvex minimization problems within the framework of abstract convexity

By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tools are the $\Phi$-convexity theory and minimax theorems for $\Phi$-convex functions. We provide conditions ensuring zero duality gap and introduce $\Phi$-Karush-Kuhn-Tucker conditions that characterize solutions to primal and dual problems. We also discuss the relationship between the dual problems introduced in the present investigation and some conjugate-type duals existing in the literature.

math.OC↗

arXiv2020

Lagrangian duality for nonconvex optimization problems with abstract convex functions

We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $Φ$-convexity theory and minimax theorem for $Φ$-convex functions. We provide conditions for zero duality gap and strong duality. Among the classes of functions, to which our duality results can be applied, are prox-bounded functions, DC functions, weakly convex functions and paraconvex functions.

math.OC↗

arXiv2020

On global properties of lower semicontinuous quadratically minorized functions

We use the framework of a type of abstract convexity ($Φ_{lsc}$-convexity) to investigate properties of lower semicontinuous quadratically minorized functions in Hilbert spaces. A new result, which states that, for every local $Φ_{lsc}$-subgradient there exists a global one is proved and plays a crucial role in our considerations. We deliver conditions for abstract subdifferentiability ($Φ_{lsc}$-subdifferentiability) of locally $C^{1,1}$ functions, twice continuously differentiable functions, prox-regular functions and paraconvex functions. As an application we establish a new sufficient and necessary condition for minimax equality for $Φ_{lsc}$-convex functions. This new condition is expressed in therms of $Φ_{lsc}$-subdifferential.

math.OC↗

arXiv2017

Minimax theorems for convex functions

In this paper provide sufficient and necessary conditions for the minimax equality for extended-valued $Φ$-convex functions. As an application we establish sufficient and necessary conditions for the minimax equality for convex-concave functions.

math.OC↗

arXiv2016

On minimax theorems for lower semicontinuous functions in Hilbert spaces

We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $Φ$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $Φ$-convex functions. These conditions are expressed in terms of abstract $Φ$-subgradients.

math.OC↗