相关论文: Complete Solutions and Triality Theory to a Noncon…

A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…

DY Gao solely or together with some of his collaborators applied his Canonical duality theory (CDT) for solving a class of unconstrained optimization problems, getting the so-called "triality theorems". Unfortunately, the "double-min…

This paper presents a canonical dual approach for solving nonconvex quadratic minimization problem. By using the canonical duality theory, nonconvex primal minimization problems over n-dimensional Lorentz cone can be transformed into…

This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem…

Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…

We present new results on optimization problems where the involved functions are evenly convex. By means of a generalized conjugation scheme and the perturbation theory introduced by Rockafellar, we propose an alternative dual problem for a…

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…

This paper presents a pure complementary energy variational method for solving anti-plane shear problem in finite elasticity. Based on the canonical duality-triality theory developed by the author, the nonlinear/nonconex partial…

Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…

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…

We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…

This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex…

The paper introduces several new concepts for solving nonconvex or nonsmooth optimization problems, including convertible nonconvex function, exact convertible nonconvex function and differentiable convertible nonconvex function. It is…

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.…

Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…

Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…

Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is…