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In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…

Theorem provers has been used extensively in software engineering for software testing or verification. However, software is now so large and complex that additional architecture is needed to guide theorem provers as they try to generate…

We present MXtalTools, a flexible Python package for the data-driven modelling of molecular crystals, facilitating machine learning studies of the molecular solid state. MXtalTools comprises several classes of utilities: (1) synthesis,…

We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower…

Large Language Models have achieved strong performance on reasoning tasks, solving competition-level coding and math problems. However, their scalability is limited by human-labeled datasets and the lack of large-scale, challenging coding…

We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…

Instruction-tuned large language models (LLMs) excel at many tasks but often fail to use external tools due to complicated and unfamiliar syntax constraints. While extensive fine-tuning and prompting can mitigate the issue, these approaches…

Existing low-bit Microscaling (MX) formats, such as MXFP4, often suffer from substantial accuracy degradation due to the use of a shared scaling factor with the Power-of-Two format. In this work, we explore strategies that introduce minimal…

Frontier Large language models (LLMs) like ChatGPT and Gemini can decipher cryptic compiler errors for novice programmers, but their computational scale, cost, and tendency to over-assist make them problematic for widespread pedagogical…

We are faced with convex quadratic programing in many contexts related to control theory, economy and robotics. In this paper, we introduce a new active set algorithm for solving such problems and analyze its possible advantages. The…

Although LLMs are capable of generating functionally correct code, they also tend to produce less energy-efficient code in comparison to human-written solutions. As these inefficiencies lead to higher computational overhead, they are in…

This paper is an overview of Image Processing and Analysis using Scilab, a free prototyping environment for numerical calculations similar to Matlab. We demonstrate the capabilities of SIP -- the Scilab Image Processing Toolbox -- which…

Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…

We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…

We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…

GPUs and other accelerators are popular devices for accelerating compute-intensive, parallelizable applications. However, programming these devices is a difficult task. Writing efficient device code is challenging, and is typically done in…

Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The…

This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…

Large language models (LLMs) underpin interactive multimedia applications such as captioning, retrieval, recommendation, and creative content generation, yet their autoregressive decoding incurs substantial latency. Speculative decoding…

Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…