Related papers: Canonical duality for solving general nonconvex co…
This paper presents an application of Canonical duality theory to the solution of contact problems with Coulomb friction. The contact problem is formulated as a quasi-variational inequality which solution is found by solving its…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
We propose to solve large instances of the non-convex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total…
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived.…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…
We develop a unified theory of augmented Lagrangians for nonconvex optimization problems that encompasses both duality theory and convergence analysis of primal-dual augmented Lagrangian methods in the infinite dimensional setting. Our goal…
A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…
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…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of fourth-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based…
Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study 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…
By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be…
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…
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…
This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. The problem is first transformed into a problem with quadratic objective and 0-1 integer variables.…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
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…
This paper demonstrates a mathematically correct and computationally powerful method for solving 3D topology optimization problems. This method is based on canonical duality theory (CDT) developed by Gao in nonconvex mechanics and global…