Related papers: Global and Robust Optimization for Non-Convex Quad…
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
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…
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 article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
In this paper, we concentrate on a particular category of quadratically constrained quadratic programming (QCQP): nonconvex QCQP with one equality constraint. This type of QCQP problem optimizes a quadratic objective under a fixed…
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…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
We present a novel efficient theoretical and numerical framework for solving global non-convex polynomial optimization problems. We analytically demonstrate that such problems can be efficiently reformulated using a non-linear objective…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…