This paper is on the portfolio optimization problem for which two generic models are presented in the context of a proprietary solver called GENO: the first is a pseudo-dynamic model meant for the single holding-period case; the second is a truly dynamic model that applies to both the single and the multi-period scenario. Both models … Read more
In this paper we obtained new approach for the problem, which it is described in reference[1,2]. In the references [1], the authors are studied Decomposition of Linear-Quadratic optimal Control problems for Two-Steps Systems. In [1], the authors assumed the switching point is fixed and it is given algorithm for solving Linear-Quadratic optimal Control problem. But … Read more
We present local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange multiplier (which is weaker than second-order sufficiency). Local superlinear convergence is established under the … Read more
The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to regain feasibility. The latter poses a computational difficulty and, therefore, the projected subgradient method is applicable only when the feasible region is “simple … Read more
We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new … Read more
DC Programming and DCA have been introduced by Pham Dinh Tao in 1986 and extensively developed by Le Thi Hoai An and Pham Dinh Tao since 1993. These approaches have been successfully applied to solving real life problems in their large scale setting. In this paper, by using the Lojasiewicz inequality for nonsmooth subanalytic functions, … Read more
We present a generic iterative scheduling procedure for the scheduling of a real flexible job shop, the so-called multitask cell at GKN Aerospace Engine Systems in Sweden. A time-indexed formulation of the problem is presented including side constraints regarding preventive maintenance, fixture availability, and unmanned night shifts. This paper continues the work in Thörnblad et … Read more
We present new models, numerical simulations and rigorous analysis for the optimization of the velocity in a race. In a seminal paper, Keller (1973,1974) explained how a runner should determine his speed in order to run a given distance in the shortest time. We extend this analysis, based on the equation of motion and aerobic … Read more
The algorithm proposed in [Mitsos Optimization 2011] for the global optimization of semi-infinite programs is extended to the global optimization of generalized semi-infinite programs (GSIP). No convexity or concavity assumptions are made. The algorithm employs convergent lower and upper bounds which are based on regular (in general nonconvex) nonlinear programs (NLP) solved by a (black-box) … Read more
We investigate the efficiency of a discretization procedure utilizing a time-indexed mathematical optimization model for finding accurate solutions to flexible job shop scheduling problems considering objectives comprising the makespan and the tardiness of jobs, respectively. The time-indexed model is used to find solutions to these problems by iteratively employing time steps of decreasing length. The … Read more