Related papers: Continuous-Time Linear Optimization
In this paper, we introduce a kind of approximate Karush--Kuhn--Tucker condition (AKKT) for a smooth cone-constrained vector optimization problem. We show that, without any constraint qualification, the AKKT condition is a necessary for a…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
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…
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…
In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
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…
The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…
The asymptotic Karush-Kuhn-Tucker (AKKT) optimality conditions are distinguished from other approaches in the literature by virtue of their capacity to be effectively derived through numerical methods, such as the utilization of an…
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…
In the recent paper of Giorgi, Jim\'enez and Novo (J Optim Theory Appl 171:70--89, 2016), the authors introduced the so-called approximate Karush-Kuhn-Tucker (AKKT) condition for smooth multiobjective optimization problems and obtained some…
Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the…
This paper presents tractable reformulations of topology optimization problems of structures subject to frictionless unilateral contact conditions. Specifically, we consider stiffness maximization problems of trusses and continua. Based on…
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 generalize the successive continuation paradigm introduced by Kern\'evez and Doedel [16] for locating locally optimal solutions of constrained optimization problems to the case of simultaneous equality and inequality constraints. The…
In this article we consider a convex feasible set described by inequality constraints that are continuous and not necessarily Lipschitz or convex. We show that if the Slater constraint qualification and a non-degeneracy condition are…
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…
This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and…
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse…
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…