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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…
Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
In recent years, several branch-and-bound (BnB) algorithms have been proposed to globally optimize rigid registration problems. In this paper, we suggest a general framework to improve upon the BnB approach, which we name Quasi BnB. Quasi…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Block majorization-minimization (BMM) is a simple iterative algorithm for nonconvex optimization that sequentially minimizes a majorizing surrogate of the objective function in each block coordinate while the other block coordinates are…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives. The algorithm also works for certain classes of non-linear programming problems.…
In this article we intend to develop a simple and implementable algorithm for minimizing a convex function over the solution set of another convex optimization problem. Such a problem is often referred to as a simple bilevel programming…
We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
We present the Branch-and-Bound Performance Estimation Programming (BnB-PEP), a unified methodology for constructing optimal first-order methods for convex and nonconvex optimization. BnB-PEP poses the problem of finding the optimal…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
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…