Search

Optimization models and methods have been used extensively in the forest industry. In this paper we describe the general wood-flow in forestry and a variety of planning problems. These cover planning periods from a fraction of a second to more than one hundred years. The problems are modelled using linear, integer and nonlinear models. Solution methods used depend on the required solution time and include for example dynamic programming, LP methods, branch & bound methods, heuristics and column generation. The importance of modelling and qualitative information is also discussed. [ABSTRACT FROM AUTHOR]

In this paper we derive necessary and sufficient conditions for some problems of global minimization. Our approach is based on methods of abstract convexity: we use a representation of an upper semicontinuous function as the lower envelope of a family of convex functions. We discuss applications of conditions obtained to the examination of some tractable sufficient conditions for the global minimum and to the theory of inequalities. [ABSTRACT FROM AUTHOR]

The sample-path method is one of the most important tools in simulation-based optimization. The basic idea of the method is to approximate the expected simulation output by the average of sample observations with a common random number sequence. In this paper, we describe a new variant of Powell’s unconstrained optimization by quadratic approximation (UOBYQA) method, which integrates a Bayesian variable-number sample-path (VNSP) scheme to choose appropriate number of samples at each iteration. The statistically accurate scheme determines the number of simulation runs, and guarantees the global convergence of the algorithm. The VNSP scheme saves a significant amount of simulation operations compared to general purpose ‘fixed-number’ sample-path methods. We present numerical results based on the new algorithm. [ABSTRACT FROM AUTHOR]

In the last two decades, the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization. These advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential. This paper focuses on two such fields: digital signal processing and communication. In the past, the widely used optimization methods in both fields had been the gradient descent or least squares methods, both of which are known to suffer from the usual headaches of stepsize selection, algorithm initialization and local minima. With the recent advances in conic and robust optimization, the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication. This paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields. The successful applications considered in this paper include adaptive filtering, robust beamforming, design and analysis of multi-user communication system, channel equalization, decoding and detection. Throughout, our emphasis is on how to exploit the hidden convexity, convex reformulation of semi-infinite constraints, analysis of convergence, complexity and performance, as well as efficient practical implementation. [ABSTRACT FROM AUTHOR]

In this paper we study optimization problems with second-order stochastic dominance constraints. This class of problems allows for the modeling of optimization problems where a risk-averse decision maker wants to ensure that the solution produced by the model dominates certain benchmarks. Here we deal with the case of multi-variate stochastic dominance under general distributions and nonlinear functions. We introduce the concept of $${\mathcal{C}}$$-dominance, which generalizes some notions of multi-variate dominance found in the literature. We apply the Sample Average Approximation (SAA) method to this problem, which results in a semi-infinite program, and study asymptotic convergence of optimal values and optimal solutions, as well as the rate of convergence of the feasibility set of the resulting semi-infinite program as the sample size goes to infinity. We develop a finitely convergent method to find an $${\epsilon}$$-optimal solution of the SAA problem. An important aspect of our contribution is the construction of practical statistical lower and upper bounds for the true optimal objective value. We also show that the bounds are asymptotically tight as the sample size goes to infinity. [ABSTRACT FROM AUTHOR]

The aim of this paper is the study of different approaches to combine and scale, in an efficient manner, descent information for the solution of unconstrained optimization problems. We consider the situation in which different directions are available in a given iteration, and we wish to analyze how to combine these directions in order to provide a method more efficient and robust than the standard Newton approach. In particular, we will focus on the scaling process that should be carried out before combining the directions. We derive some theoretical results regarding the conditions necessary to ensure the convergence of combination procedures following schemes similar to our proposals. Finally, we conduct some computational experiments to compare these proposals with a modified Newton's method and other procedures in the literature for the combination of information. [ABSTRACT FROM AUTHOR]

Mean-risk models have been widely used in portfolio optimization. However, such models may produce portfolios that are dominated with respect to second order stochastic dominance and therefore not optimal for rational and risk-averse investors. This paper considers the problem of constructing a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution has specified desirable properties. The problem is multi-objective and is transformed into a single objective problem by using the reference point method, in which target levels, known as aspiration points, are specified for the objective functions. A model is proposed in which the aspiration points relate to ordered outcomes for the portfolio return. This concept is extended by additionally specifying reservation points, which act pre-emptively in the optimization model. The theoretical properties of the models are studied. The performance of the models on real data drawn from the Hang Seng index is also investigated. [ABSTRACT FROM AUTHOR]

In this paper we discuss the level set method of Joó and how to use it to give an elementary proof of the well-known minimax theorem of Sion. Although this proof technique was initiated by Joó and based on the intersection of upper level sets and a clever use of the topological notion of connectedness, it is not very well known and accessible for researchers in optimization. At the same time we simplify the original proof of Joó and give a more elementary proof of the celebrated minimax theorem of Sion. [ABSTRACT FROM AUTHOR]

In this work nonlinear non-convex multiobjective bilevel optimization problems are discussed using an optimistic approach. It is shown that the set of feasible points of the upper level function, the so-called induced set, can be expressed as the set of minimal solutions of a multiobjective optimization problem. This artificial problem is solved by using a scalarization approach by Pascoletti and Serafini combined with an adaptive parameter control based on sensitivity results for this problem. The bilevel optimization problem is then solved by an iterative process using again sensitivity theorems for exploring the induced set and the whole efficient set is approximated. For the case of bicriteria optimization problems on both levels and for a one dimensional upper level variable, an algorithm is presented for the first time and applied to two problems: a theoretical example and a problem arising in applications. [ABSTRACT FROM AUTHOR]

We introduce the regularized Newton method (rnm) for unconstrained convex optimization. For any convex function, with a bounded optimal set, the rnm generates a sequence that converges to the optimal set from any starting point. Moreover the rnm requires neither strong convexity nor smoothness properties in the entire space. If the function is strongly convex and smooth enough in the neighborhood of the solution then the rnm sequence converges to the unique solution with asymptotic quadratic rate. We characterized the neighborhood of the solution where the quadratic rate occurs. [ABSTRACT FROM AUTHOR]

Traveling Salesman, Steiner Tree, and many other famous geometric optimization problems are NP-hard. Since we do not expect to design efficient algorithms that solve these problems optimally, researchers have tried to design approximation algorithms, which can compute a provably near-optimal solution in polynomial time.We survey such algorithms, in particular a new technique developed over the past few years that allows us to design approximation schemes for many of these problems. For any fixed constant c> 0, the algorithm can compute a solution whose cost is at most (1 + c) times the optimum. (The running time is polynomial for every fixed c> 0, and in many cases is even nearly linear.) We describe how these schemes are designed, and survey the status of a large number of problems. [ABSTRACT FROM AUTHOR]