Related papers: A duality principle for non-convex optimization in…
General nonconvex optimization problems are studied by using the canonical duality-triality theory. The triality theory is proved for sums of exponentials and quartic polynomials, which solved an open problem left in 2003. This theory can…
A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
The main purpose of this research note is to show that the triality theory can always be used to identify both global minimizer and the biggest local maximizer in global optimization. An open problem left on the double-min duality is solved…
Distributed and decentralized optimization are key for the control of networked systems. Application examples include distributed model predictive control and distributed sensing or estimation. Non-linear systems, however, lead to problems…
This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in DOI 10.1007/s11228-019-00515-2. It provides an existence theorem for primal optimal solutions and, under…
Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…
The canonical duality theory has provided with a unified analytic solution to a range of discrete and continuous problems in global optimization, which can transform a nonconvex primal problem to a concave maximization dual problem over a…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
This paper studies duality and optimality conditions in general convex stochastic optimization problems introduced by Rockafellar and Wets in 1976. We derive an explicit dual problem in terms of two dual variables, one of which is the…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
For the existence of strong duality in convex optimization regularity conditions play an indisputable role. We mainly deal in this paper with regularity conditions formulated by means of different generalizations of the notion of interior…
Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications.…
The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…