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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…
Decision-focused learning is a promising development for contextual optimisation. It enables us to train prediction models that reflect the contextual sensitivity structure of the problem. However, there have been limited attempts to extend…
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first…
We develop a new interior-point algorithm for solving multiconic optimization problems using the parabolic target space approach. The feasible cone in these problems is composed as a direct product of many small-dimensional cones. Our…
Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…
One of the keys to flying quadrotors is to optimize their trajectories within the set of collision-free corridors. These corridors impose nonconvex constraints on the trajectories, making real-time trajectory optimization challenging. We…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…
We note that known methods achieving the optimal oracle complexity for first order convex optimization require quadratic memory, and ask whether this is necessary, and more broadly seek to characterize the minimax number of first order…
Join order optimization is among the most crucial query optimization problems, and its central position is also evident in the new research field where quantum computing is applied to database optimization and data management. In the field,…
We present a GPU-accelerated backend for QOCO, a C-based solver for quadratic objective second-order cone programs (SOCPs) based on a primal-dual interior point method. Our backend uses NVIDIA's cuDSS library to perform a direct sparse LDL…
Combining quantum computers with classical compute power has become a standard means for developing algorithms that are eventually supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or…
Optimization problems with set-valued objective functions arise in contexts such as multi-stage optimization with vector-valued objectives. The aim is to identify an optimizer -- a feasible point with an optimal objective value -- based on…
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…