in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

The synthesis of complex distillation columns has remained a major challenge since the pioneering work by [Sargent, R.W.H., & Gaminibandara, K. (1976). Optimal design of plate distillation columns. In L.C.W. Dixon (Ed.), Optimization in action. New York: Academic Press]. In this paper, we first provide a review of recent work for the optimal design of distillation of individual columns using tr...

Nonlinear programming (NLP) has been a key enabling tool for model-based decision-making in the chemical industry for over 50 years. Optimization is frequently applied in numerous areas of chemical engineering including the development of process models from experimental data, design of process flowsheets and equipment, planning and scheduling of chemical process operations, and the analysis of...

in this paper, the portfolio selection problem is considered, where fuzziness and randomness appear simultaneously in optimization process. since return and dividend play an important role in such problems, a new model is developed in a mixed environment by incorporating fuzzy random variable as multi-objective nonlinear model. then a novel interactive approach is proposed to determine the pref...

Interior point methods for nonlinear programs (NLP) are adapted for solution of mathematical programs with complementarity constraints (MPCCs). The constraints of the MPCC are suitably relaxed so as to guarantee a strictly feasible interior for the inequality constraints. The standard primal-dual algorithm has been adapted with a modified step calculation. The algorithm is shown to be superline...

It is challenging to generate optimal trajectories for nonlinear dynamic systems under external disturbances. In this brief, we present a novel approach planning safe of the chance-constrained trajectory optimization problems with nonconvex constraints. First, chance constraints are handled by deterministic ones which show its availability. We derive an iterative convex method solve control pro...

Cloud Computing provides a appropriate on-demand network access to a shared pool of configurable computing resources which could be rapidly deployed with much more great efficiency and with minimal overhead to management. This paper deals with the secure outsourcing of nonlinear programming. It provides a practical mechanism design which fulfils input/output privacy, cheating resilience, and ef...

A literature survey from the area of nonlinear model predictive control (MPC) is presented. After a brief review of the main characteristics of linear MPC algorithms various classes of nonlinear MPC algorithms based on state-space models, such as nonlinear extensions of dynamic matrix control (DMC), Newton-type algorithms and nonlinear programming (NLP) based algorithms are discussed. These alg...

The strategy of dynamic programming reduces the complexity of a search problem which decomposes into frequently-reused instances of the same problem. You encountered dynamic programming for n-gram segmentation in HW4. We have also discussed two more dynamic programming algorithms in lecture: Viterbi and forward-backward. For HW5, you will need to implement the Viterbi algorithm. The forward-bac...