arXiv subjects

Luka Rutešić

Publications and source records attributed to Luka Rutešić.

3 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.

math.OC↗

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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arXiv2026

ASMOP: Additional sampling stochastic trust region method for multi-objective problems

We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size and the acceptance of a candidate point. Depending on the problem, the method can yield a mini-batch or an increasing sample size behavior. This work can be viewed as an extension of additional sampling trust region method for scalar finite sum function minimization presented in the literature, requiring nontrivial modifications both in construction and in convergence analysis of the algorithm. Under assumptions standard for this framework, we prove stochastic convergence for twice continuously-differentiable, but possibly non-convex objective functions. The experiments on machine learning binary classification datasets show the efficiency of the proposed scheme and its competitiveness with the relevant state-of-the-art methods in both convex and non-convex setup.

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