Mirror Descent Methods for Quasar Convex Optimization Problems With Non-Smooth Inequality Constraints

2026/05/14 by Mohammad Alkousa
#math.OC

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Abstract

In this paper, we consider constraint optimization problems subject to non-smooth convex functional (inequality-type) constraints, wherein the objective function is non-smooth and quasar convex. We propose and analyze two groups of algorithms, each consisting of a standard version and a modified variant, that operate by switching between two types of iteration points: productive and non-productive. Within each group, we develop distinct mirror descent-type algorithms for both deterministic and stochastic settings, and we establish their convergence rates.

Citations

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• Accelerated Methods for α-Weakly-Quasi-Convex Problems
• Adaptive Stochastic Mirror Descent for Constrained Optimization
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Related

• Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints
• Smooth Quasar-Convex Optimization with Constraints
• Adaptive Mirror Descent for Constrained Optimization
• On The Convergence of First Order Methods for Quasar-Convex Optimization
• On Modification of an Adaptive Stochastic Mirror Descent Algorithm for Convex Optimization Problems with Functional Constraints