arXiv subjects

Nataša Krejić

Publications and source records attributed to Nataša Krejić.

8 recordsLinked to original sources

arXiv2026

IPAS: An Adaptive Sample Size Method for Weighted Finite Sum Problems with Linear Equality Constraints

Optimization problems with the objective function in the form of weighted sum and linear equality constraints are considered. Given that the number of local cost functions can be large as well as the number of constraints, a stochastic optimization method is proposed. The method belongs to the class of variable sample size first order methods, where the sample size is adaptive and governed by the additional sampling technique earlier proposed in the unconstrained optimization framework. The resulting algorithm may be a mini-batch method, increasing sample size method, or even deterministic in a sense that it eventually reaches the full sample size, depending on the problem and similarity of the local cost functions. Regarding the constraints, the method uses controlled, but inexact projections on the feasible set, yielding possibly infeasible iterates. Almost sure convergence is proved under some standard assumptions for the stochastic framework, without imposing the convexity. Numerical results on relevant machine learning experiments, i.e., real-world data sets for logistic regression problems, show that the proposed algorithm is competitive with the state-of-the-art methods.

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arXiv2026

SMOP: Stochastic trust region method for multi-objective problems

The problem we consider is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate functions and gradients. The key novelty is approximation of each function in the multiobjective problem with probabilistically fully linear model which yields the composite model defined by max operator as a satisfactory approximation for the nonsmooth scalarized objective function. We prove the almost sure convergence of the proposed algorithm to a Pareto critical point. Numerical results demonstrate effectiveness of the probabilistic trust region by comparing it to competitive stochastic multi-objective solvers. The application in supervised machine learning is showcased by training non discriminatory Logistic Regression models on different size data groups. Additionally, we use several test examples with irregularly shaped fronts to exhibit the efficiency of the algorithm

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arXiv2025

AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints

A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (\text{A}ddi\-ti\-onal \text{S}ampling for \text{BOX} constraints), that combines projected gradient directions with adaptive variable sample size strategies and nonmonotone line search. The method dynamically adjusts the batch size based on progress with respect to the additional sampling function and on structural consistency of the projected direction, enabling practical adaptivity of AS-BOX, while ensuring theoretical support. We establish almost sure convergence under standard assumptions and provide complexity bounds. Numerical experiments demonstrate the efficiency and competitiveness of the proposed method compared to state-of-the-art algorithms.

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arXiv2025

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints

We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one end, to increasing sample size that achieves the full sample eventually, on the other end of the spectrum. A non-monotone line search is used for the step size update, while the penalty parameter is also adaptive. The proposed algorithm avoids costly projections, which, together with the sample size update, may yield significant computational cost savings. Also, the proposed method can be viewed as a transition of an additional sampling approach for unconstrained and linear constrained problems, to a more general class with non-linear constraints. The almost sure convergence is proved under a standard set of assumptions for this framework, while numerical experiments on both academic and real-data based machine learning problems demonstrate the effectiveness of the proposed approach.

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arXiv2024

SLiSeS: Subsampled Line Search Spectral Gradient Method for Finite Sums

The spectral gradient method is known to be a powerful low-cost tool for solving large-scale optimization problems. In this paper, our goal is to exploit its advantages in the stochastic optimization framework, especially in the case of mini-batch subsampling that is often used in big data settings. To allow the spectral coefficient to properly explore the underlying approximate Hessian spectrum, we keep the same subsample for several iterations before subsampling again. We analyze the required algorithmic features and the conditions for almost sure convergence, and present initial numerical results that show the advantages of the proposed method.

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arXiv2022

A low-cost alternating projection approach for a continuous formulation of convex and cardinality constrained optimization

We consider convex constrained optimization problems that also include a cardinality constraint. In general, optimization problems with cardinality constraints are difficult mathematical programs which are usually solved by global techniques from discrete optimization. We assume that the region defined by the convex constraints can be written as the intersection of a finite collection of convex sets, such that it is easy and inexpensive to project onto each one of them (e.g., boxes, hyper-planes, or half-spaces). Taking advantage of a recently developed continuous reformulation that relaxes the cardinality constraint, we propose a specialized penalty gradient projection scheme combined with alternating projection ideas to solve these problems. To illustrate the combined scheme, we focus on the standard mean-variance portfolio optimization problem for which we can only invest in a preestablished limited number of assets. For these portfolio problems with cardinality constraints we present a numerical study on a variety of data sets involving real-world capital market indices from major stock markets. On those data sets we illustrate the computational performance of the proposed scheme to produce the effective frontiers for different values of the limited number of allowed assets.

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arXiv2022

LSOS: Line-search Second-Order Stochastic optimization methods for nonconvex finite sums

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at each iteration, which allows us to control the error present in the line-search procedure. Stationarity of limit points is proved in the almost-sure sense, while almost-sure convergence of the sequence of approximations to the solution holds with the additional hypothesis that the functions are strongly convex. Numerical experiments, including comparisons with state-of-the art stochastic optimization methods, show the efficiency of our approach.

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arXiv2021

Tax Evasion Risk Management Using a Hybrid Unsupervised Outlier Detection Method

Big data methods are becoming an important tool for tax fraud detection around the world. Unsupervised learning approach is the dominant framework due to the lack of label and ground truth in corresponding data sets although these methods suffer from low interpretability. HUNOD, a novel hybrid unsupervised outlier detection method for tax evasion risk management, is presented in this paper. In contrast to previous methods proposed in the literature, the HUNOD method combines two outlier detection approaches based on two different machine learning designs (i.e, clustering and representational learning) to detect and internally validate outliers in a given tax dataset. The HUNOD method allows its users to incorporate relevant domain knowledge into both constituent outlier detection approaches in order to detect outliers relevant for a given economic context. The interpretability of obtained outliers is achieved by training explainable-by-design surrogate models over results of unsupervised outlier detection methods. The experimental evaluation of the HUNOD method is conducted on two datasets derived from the database on individual personal income tax declarations collected by the Tax Administration of Serbia. The obtained results show that the method indicates between 90% and 98% internally validated outliers depending on the clustering configuration and employed regularization mechanisms for representational learning.

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