Related papers: Implementing a unified solver for nonlinearly cons…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
This tutorial offers a quick, hands-on introduction to solving Quadratic Unconstrained Binary Optimization (QUBO) models on currently available quantum computers and their simulators. We cover both IBM and D-Wave machines: IBM utilizes a…
We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive…
This paper considers global optimization with a black-box unknown objective function that can be non-convex and non-differentiable. Such a difficult optimization problem arises in many real-world applications, such as parameter tuning in…
Quadratic Unconstrained Binary Optimization (QUBO) is a versatile framework for modeling combinatorial optimization problems. This study benchmarks five software-based QUBO solvers: Neal, PyTorch (CPU), PyTorch (GPU), JAX, and SciPy, on…
We present a novel method for neural network quantization that emulates a non-uniform $k$-quantile quantizer, which adapts to the distribution of the quantized parameters. Our approach provides a novel alternative to the existing uniform…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…
Text-to-image latent diffusion models (LDMs) have recently emerged as powerful generative models with great potential for solving inverse problems in imaging. However, leveraging such models in a Plug & Play (PnP), zero-shot manner remains…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
Interior Point Methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due…
Combinatorial optimization problems arise in logistics, scheduling, and resource allocation, yet existing approaches face a fundamental trade-off among generality, performance, and usability. We present cuGenOpt, a GPU-accelerated…
We consider distributed nonconvex optimization over an undirected network, where each node privately possesses its local objective and communicates exclusively with its neighboring nodes, striving to collectively achieve a common optimal…
To solve unmodeled optimization problems with hard constraints, this paper proposes a novel zeroth-order approach called Safe Zeroth-order Optimization using Linear Programs (SZO-LP). The SZO-LP method solves a linear program in each…
The LogQ algorithm encodes Quadratic Unconstrained Binary Optimization (QUBO) problems, which are often encountered in the industry (portfolio optimization, fleet optimization, charging stations, etc.). It was developed within the framework…
Visual navigation is a fundamental problem in embodied AI, yet practical deployments demand long-horizon planning capabilities to address multi-objective tasks. A major bottleneck is data scarcity: policies learned from limited data often…
This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly…
Quantum approximate optimization is one of the promising candidates for useful quantum computation, particularly in the context of finding approximate solutions to Quadratic Unconstrained Binary Optimization (QUBO) problems. However, the…
Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to…