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An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…
We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be…
We describe general heuristics to approximately solve a wide variety of problems with convex objective and decision variables from a nonconvex set. The heuristics, which employ convex relaxations, convex restrictions, local neighbor search…
This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…
The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this work, we combine techniques from both fields to address the problem of learning to…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
Significant advancements have been made in the capabilities of code large language models, leading to their rapid adoption and application across a wide range of domains. However, their further advancements are often constrained by the…
We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in…
We propose a new class of convex penalty functions, called \emph{variational Gram functions} (VGFs), that can promote pairwise relations, such as orthogonality, among a set of vectors in a vector space. These functions can serve as…
Test-time scaling has emerged as a promising approach for improving code generation by exploring large solution spaces at inference time. However, existing methods often rely on public test cases that are unavailable in practice, or require…
We describe an intelligent assistant based on mining existing software repositories to help the developer interactively create checkable specifications of code. To be most useful we apply this at the subsystem level, that is chunks of code…
Nonlinear (deterministic and stochastic) optimal control problems are often solved on embedded devices using first-order numerical optimisation methods. The gradient computation accounts for a significant part of the computation cost per…
Contextual Partitioning introduces an innovative approach to enhancing the architectural design of large-scale computational models through the dynamic segmentation of parameters into context-aware regions. This methodology emphasizes the…
A parametrized convex function depends on a variable and a parameter, and is convex in the variable for any valid value of the parameter. Such functions can be used to specify parametrized convex optimization problems, i.e., a convex…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
Large pre-trained code generation models, such as OpenAI Codex, can generate syntax- and function-correct code, making the coding of programmers more productive and our pursuit of artificial general intelligence closer. In this paper, we…
Generating software from abstract models is a prime activity in model-drivenengineering. Adaptable and extendable code generators are important to address changing technologies as well as user needs. However, theyare less established, as…
Graph algorithms are at the heart of several applications, and achieving high performance with them has become critical due to the tremendous growth of irregular data. However, irregular algorithms are quite challenging to parallelize…
Cooper is an open-source package for solving constrained optimization problems involving deep learning models. Cooper implements several Lagrangian-based first-order update schemes, making it easy to combine constrained optimization…