In this paper, we study some discrete-time portfolio optimization problems. We introduce a discrete-time financial market model. The change in asset prices is modelled in contrast to the continuous-time market model by stochastic difference equations. We provide solutions of these stochastic difference equations. Then we introduce the discrete-time risk measures and the portfolio optimization p...

Dense image matching is a fundamental lowlevel problem in Computer Vision, which has received tremendous attention from both discrete and continuous optimization communities. The goal of this paper is to combine the advantages of discrete and continuous optimization in a coherent framework. We devise a model based on energy minimization, to be optimized by both discrete and continuous algorithm...

This paper considers structural optimization problems featuring discrete variables, as well as nonlinear implicit constraints which can only be evaluated through time-expensive computations. A prominent application consists in the preliminary structural design of large ships, where many of the variables take their values in discrete sets which model standard element dimensions to be selected fr...

A matroid is a mathematical structure that generalizes the notion of linear independence. Remarkably, this simple and elegant mathematical structure can be used to systematically develop efficient and simple “greedy” algorithms for a variety of discrete optimization problems. Moreover, matroids provide some insight into why other discrete optimization problems are apparently computationally int...

The optimal reactive power dispatch (ORPD) is a very important problem aspect of power system planning and is a highly nonlinear, non-convex optimization problem because consist of both continuous and discrete control variables. Since the power system has inherent uncertainty, hereby, this paper presents both of the deterministic and stochastic models for ORPD problem in multi objective and sin...

In the present study the efficiency of Big Bang-Big Crunch (BB-BC) algorithm is investigated in discrete structural design optimization. It is shown that a standard version of the BB-BC algorithm is sometimes unable to produce reasonable solutions to problems from discrete structural design optimization. Two reformulations of the algorithm, which are referred to as modified BB-BC (MBB-BC) and e...

We introduce a novel discrete optimization method for training in the context of a boosting framework for large scale binary classifiers. The motivation is to cast the training problem into the format required by existing adiabatic quantum hardware. First we provide theoretical arguments concerning the transformation of an originally continuous optimization problem into one with discrete variab...

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and constraints that represent the discrete...

This contribution presents a method for the simultaneous economic optimization and optimal design for disturbance rejection of discrete time systems. The method is an extension of a previously presented approach for the optimization of discrete time systems with constraints on robust stability [10]. In this contribution we extend the method to a new set of constraints on the location of poles o...