Related papers: Solving a new type of quadratic optimization probl…
When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
In this paper we consider convex optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum…
Quadratically constrained quadratic programs (QCQPs) are an expressive family of optimization problems that occur naturally in many applications. It is often of interest to seek out sparse solutions, where many of the entries of the…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
Decades of advances in mixed-integer linear programming (MILP) and recent development in mixed-integer second-order-cone programming (MISOCP) have translated very mildly to progresses in global solving nonconvex mixed-integer quadratically…
We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
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…
We are faced with convex quadratic programing in many contexts related to control theory, economy and robotics. In this paper, we introduce a new active set algorithm for solving such problems and analyze its possible advantages. The…
The MaxCut problem is a fundamental problem in Combinatorial Optimization, with significant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
This paper presents a canonical dual approach to the problem of minimizing the sum of a quadratic function and the ratio of nonconvex function and quadratic functions, which is a type of non-convex optimization problem subject to an…
We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…
A novel approach is introduced to a very widely occurring problem, providing a complete, explicit resolution of it: minimisation of a convex quadratic under a general quadratic, equality or inequality, constraint. Completeness comes via…
In this paper, we present a novel method for solving a class of quadratically constrained quadratic optimization problems using only additions and multiplications. This approach enables solving constrained optimization problems on private…
The objective function of a quadratic combinatorial optimization problem (QCOP) can be represented by two data points, a quadratic cost matrix Q and a linear cost vector c. Different, but equivalent, representations of the pair (Q, c) for…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
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…