Mathematical Optimization
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Related Articles from SNS
Semantic Constraint Synthesis for Adaptive Trajectory Optimization via Large Language Models
arXiv:2606.04123v1 Announce Type: cross Abstract: Trajectory optimization is a critical component for enabling safe and reliable autonomous operations in space exploration. As space missions increase in frequency, complexity, and scope, there is a growing need to rapidly formulate mathematically sound trajectory optimization problems that accurately reflect mission objectives and operational constraints. However, translating mission intent into tractable analytical formulations for...
NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agents
arXiv:2601.21372v2 Announce Type: replace Abstract: We present NEMO, a system that translates Natural-language descriptions of decision problems into formal Executable Mathematical Optimization implementations using autonomous coding agents (ACAs). Existing approaches rely on specialized large language models (LLMs) or bespoke task-specific agents that are often brittle and frequently generate syntactically invalid or non-executable code. NEMO instead treats ACAs as a first-class abstraction...
Stepsize Hedging: an Alternative Mechanism for Accelerating Gradient Descent
Mathematics > Optimization and Control [Submitted on 29 May 2026] Title:Stepsize Hedging: an Alternative Mechanism for Accelerating Gradient Descent View PDFAbstract:Can gradient descent be accelerated by just choosing better stepsizes?
Stepsize Hedging: an Alternative Mechanism for Accelerating Gradient Descent
Mathematics > Optimization and Control [Submitted on 29 May 2026 (v1), last revised 2 Jun 2026 (this version, v2)] Title:Stepsize Hedging: an Alternative Mechanism for Accelerating Gradient Descent View PDFAbstract:Can gradient descent be accelerated by just choosing better stepsizes?
Cross-Layer Subspace Coupling for LLM Compression: A Unifying Framework and Its Empirical Limits
arXiv:2605.30836v2 Announce Type: replace Abstract: Recent SVD based compression methods for large language models like SVD LLM and Basis Sharing can be unified under one optimization problem. While mathematical proofs and tests on Pythia models show this unified approach improves weight reconstruction error by up to 46% percent it fails in practical tasks.
Cross-Layer Subspace Coupling for LLM Compression: A Unifying Framework and Its Empirical Limits
Announce Type: new Abstract: Recent SVD based compression methods for large language models like SVD LLM and Basis Sharing can be unified under one optimization problem. While mathematical proofs and tests on Pythia models show this unified approach improves weight reconstruction error by up to 46% percent it fails in practical tasks.
Computer-Assisted Proofs for Geometric Optimization: From Crystallization to Carbon Nanotubes
Announce Type: replace Abstract: We present a framework based on computer-assisted proofs that turns geometry optimization simulations for atomistic structures into mathematical proofs. Starting from a numerically computed approximation of a local minimizer or saddle point, we use validated numerical computations to prove the existence of a critical point of the potential energy close to this approximation. We demonstrate this framework in two settings.
Outcome-Grounded Advantage Reshaping for Fine-Grained Credit Assignment in Mathematical Reasoning
Announce Type: replace Abstract: Group Relative Policy Optimization (GRPO) has emerged as a promising critic-free reinforcement learning paradigm for reasoning tasks. However, standard GRPO employs a coarse-grained credit assignment mechanism that propagates group-level rewards uniformly to to every token in a sequence, neglecting the varying contribution of individual reasoning steps. We address this limitation by introducing Outcome-grounded Advantage Reshaping (OAR), a fine-grained credit...
MMR-GRPO: Accelerating GRPO-Style Training through Diversity-Aware Reward Reweighting
arXiv:2601.09085v2 Announce Type: replace Abstract: Group Relative Policy Optimization (GRPO) has become a standard approach for training mathematical reasoning models; however, its reliance on multiple completions per prompt makes training computationally expensive. Although recent work has reduced the number of training steps required to reach peak performance, the overall wall-clock training time often remains unchanged or even increases due to higher per-step cost. We propose MMR-GRPO,...
S3TS: Stochastic Scenario-Structured Tree Search for Advanced Planning Under Uncertainty
arXiv:2606.02151v1 Announce Type: new Abstract: Effective scheduling in the energy sector is essential to ensure the reliable operation of electrical grids and their connected assets by, for instance, optimizing the dispatch of generation units and storage systems. An effective planning strategy must (a) accommodate advanced and potentially non-linear system models -- exploiting the increasing data availability of modern grids, and (b) explicitly handle uncertainties arising, for instance,...