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The control barrier function (CBF) has become a fundamental tool in safety-critical systems design since its invention. Typically, the quadratic optimization framework is employed to accommodate CBFs, control Lyapunov functions (CLFs),…
We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including…
We present a quantum algorithm for finding the minimum of a function based on multistep quantum computation and apply it for optimization problems with continuous variables, in which the variables of the problem are discretized to form the…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…
We present a novel approach for constructing discrete optimization benchmarks that enables fine-grained control over problem properties, and such benchmarks can facilitate analyzing discrete algorithm behaviors. We build benchmark problems…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
Executing multiple tasks concurrently is important in many robotic applications. Moreover, the prioritization of tasks is essential in applications where safety-critical tasks need to precede application-related objectives, in order to…
In this paper, we consider the problem of stochastic optimization, where the objective function is in terms of the expectation of a (possibly non-convex) cost function that is parametrized by a random variable. While the convergence speed…
In this paper, a new one-parameter filled function approach is developed for nonlinear multi-objective optimization. Inspired by key filled function ideas from single-objective optimization, the proposed method is adapted to the…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
In this article, a novel barrier function is introduced to convert the box-constrained convex optimization problem to an unconstrained problem. For each double-sided bounded variable, a single monomial function is added as a barrier…
Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…
In this paper we present a reformulation--framed as a constrained optimization problem--of multi-robot tasks which are encoded through a cost function that is to be minimized. The advantages of this approach are multiple. The…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
The study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…