Related papers: Global Nonconvex Optimization with Integer Variabl…
This paper presents a proximal bundle variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Like other proximal bundle variants, RPB solves a sequence of prox bundle…
A branch and bound algorithm is developed for global optimization. Branching in the algorithm is accomplished by subdividing the feasible set using ellipses. Lower bounds are obtained by replacing the concave part of the objective function…
Most non-convex optimization theory is built around gradient dynamics, leaving global convergence largely unexplored. The dominant paradigm focuses on stationarity, certifying only that the gradient norm vanishes, which is often a weak…
Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
We use sensitivity analysis to design bounding-focused discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
We study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
This paper describes a method for solving smooth nonconvex minimization problems subject to bound constraints with good worst-case complexity guarantees and practical performance. The method contains elements of two existing methods: the…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
In this paper, we develop a new concept of Global Curvature Bound for an arbitrary nonlinear operator between abstract metric spaces. We use this notion to characterize the global complexity of high-order algorithms solving composite…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…
In this paper, we are interested in finding the global minimizer of a nonsmooth nonconvex unconstrained optimization problem. By combining the discrete consensus-based optimization (CBO) algorithm and the gradient descent method, we develop…