We study an optimization problem of an investor in which there is a better investment opportunity when he is rich than when he is poor. We model the betterment of the investment opportunity by considering an exogenously specified wealth threshold such that the investor’s investment opportunity is better when his wealth is above the threshold than when it is below the threshold. We derive a clos...

Dynamic engineering systems are playing an increasingly important role in society, especially as active and autonomous dynamic systems become more mature and prevalent across a variety of domains. Successful design of complex dynamic systems requires multidisciplinary analysis and design techniques. While multidisciplinary design optimization has been used successfully for the development of ma...

from OPEC-caused price changes.) In addition, we believe that use of regulated prices is inconsistent with the spirit of a study purporting to demonstrate the advantages of increased competition. Our second alternative question modifies the meaning of an optimally configured capital stock. We call it the dynamic optimization (DO)

—The do-not-exceed (DNE) limit method was proposed to accommodate more variable renewable generation (VRG) securely. However, the lack of involving discrete recourse control precludes this method from gaining more flexibility for better VRG integration. This letter formulates a multi-period DNE limit model considering continuous and discrete recourse controls. This model belongs to two-stage ro...

Overview Diagnosis traditionally viewed as logical reasoning – (de Kleer and Williams 87), (Reiter 87), ... But more naturally viewed as constraint optimization – Minimal set of faulty components, most likely fault, ... Framework that unifies qualitative and quantitative notions of diagnosis using semiring-based CSP – Choose appropriate semiring and construct constraints Diagnosis algorithms ba...

My thesis focuses on global optimization of nonconvex integral objective functions subject to parameter dependent ordinary differential equations. In particular, efficient, deterministic algorithms are developed for solving problems with both linear and nonlinear dynamics embedded. The techniques utilized for each problem classification are unified by an underlying composition principle transfe...

In the last chapter, we saw that greedy algorithms are efficient solutions to certain optimization problems. However, there are optimization problems for which no greedy algorithm exists. In this chapter, we will examine a more general technique, known as dynamic programming, for solving optimization problems. Dynamic programming is a technique of implementing a top-down solution using bottom-u...

The goal in external beam radiotherapy for cancer is to maximize tumor-damage while limiting toxic effects of radiation on nearby healthy anatomies. This is achieved through spatial localization and temporal dispersion of radiation dose. Once a radiation intensity profile that achieves the maximum possible spatial localization is designed at the beginning of a multi-week treatment-course, the t...

These notes are an attempt to give an overview of dynamic optimization and the solution methods used in solving dynamic optimization problems. Also, they are an attempt to highlight the connection between the different solution methods (finite horizon vs. infinite horizon or discrete vs. continuous time.) All through these notes I will use the consumption problem to illustrate solution methods ...