When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this framework is where these followers are uncooperatively making decisions while having cross reference of decision information. This situation is call...

In this paper we study nonlinear programming problems with equality, inequality, and abstract constraints where some of the functions are Fréchet differentiable at the optimal solution, some of the functions are Lipschitz near the optimal solution, and the abstract constraint set may be nonconvex. We derive Fritz John type and Karush–Kuhn–Tucker (KKT) type first order necessary optimality condi...

In the first part of this paper, inspired by the geometric method of Jean-Pierre Marec, we consider the two-impulse Hohmann transfer problem between two coplanar circular orbits as a constrained nonlinear programming problem. By using the Kuhn-Tucker theorem, we analytically prove the global optimality of the Hohmann transfer. Two sets of feasible solutions are found, one of which corresponding...

Design automation of one-of-a-kind engineering systems is considered a particularly challenging problem (Adeli 1994). Adeli and his associates have been working on creating novel design theories and computational models with two broad objectives: (1) automation and (2) optimization (Adeli and Hung 1995; Adeli and Kamal 1993; Adeli and Zhang 1993; Adeli and Yeh 1989; Adeli and Balasubramanyam 19...

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal problem that minimizes cost over finite time horizon for stochastic systems subject energy constraints. To tackle problem, propose efficient bisection line search algorithm outperforms other approaches such as semidefinite programming in terms comp...

The environmental sustainability and business benefits of end-of-life products have led to worldwide growth in the remanufacturing market. However, customers are often sceptical about quality durability remanufactured products. To ensure a risk-free customer experience, dealers carry out some upgrading actions on most critical components offer reasonable warranty period at time resale. It is cr...

Bilevel programming problems are often reformulated using the Karush-Kuhn-Tucker conditions for lower level problem resulting in a mathematical program with complementarity constraints (MPCC). First, we present KKT reformulation of bilevel optimization on Riemannian manifolds. Moreover, show that global optimal solutions theMPCCcorrespond to manifolds provided convex satisfies Slater?s constrai...

The Kuhn-Tucker and envelope theorems can be used to characterize the solution to a wide range of constrained optimization problems: static or dynamic, under perfect foresight or featuring randomness and uncertainty. In addition, these same two results provide foundations for the work on the maximum principle and dynamic programming that we will do later on. For both of these reasons, the Kuhn-...

We pose the problem of approximating optimally a given nonnegative signal with scalar autoconvolution signal. The I-divergence is chosen as optimality criterion being well suited to incorporate nonnegativity constraints. After proving existence an optimal approximation, we derive iterative descent algorithm alternating minimization type find minimizer. based on lifting technique developed by Cs...

A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucke...