Related papers: Canonical dual method for mixed integer fourth-ord…
In this paper, we develop a new framework for constructing infeasible-start primal-dual methods for Conic Optimization. Our approach can be seen as a straightforward consequence of Gordan Theorem of Alternative. Given by the target upper…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
By applying the perturbation function approach, we propose the Lagrangian and the conjugate duals for minimization problems of the sum of two, generally nonconvex, functions. The main tools are the $\Phi$-convexity theory and minimax…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…
We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…
We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
DY Gao together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of constrained optimization problems. Unfortunately, in several papers on this subject there are unclear statements, not…
We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the…
We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…
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…
Post buckling problem of a large deformed beam is analyzed using canonical dual finite element method (CD-FEM). The feature of this method is to choose correctly the canonical dual stress so that the original non-convex potential energy…
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from…
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 article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
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…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…