Array syntax, existed in many languages, adds expressive power by allowing operations on and assignments to the array sections. When compiling to a uniprocessor machine, the array statement must be converted into a loop that maintains the correct semantics, by a process called scalarization. Scalarization presents a significant technical problem because an array assignment needs to be implement...

A continuous time mean-variance (MV) problem optimizes the bi-objective criteria 5 (V, E), respectively representing variance V and expected value E of a random variable at the end 6 of a time horizon T . This problem is computationally challenging since the dynamic programming 7 principle cannot be directly applied to the variance criterion. An embedding technique has been 8 proposed in [18, 2...

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary ...

We apply a flexible Inexact-Restoration (IR) algorithm to optimization problems with multiobjective constraints under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. We show that with the IR framework there is a natural way to explor...

The paper is concerned with the optimistic formulation of a bilevel optimization problem with multiobjective lower-level problem. Considering the scalarization approach for the multiobjective program, we transform our problem into a scalar-objective optimization problem with inequality constraints by means of the well-known optimal value reformulation. Completely detailed first-order necessary ...

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multiobjective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this work we propose a variation of this method, taking into account the regularization with logarithm and quasi-distance, wher...

We use the idea of a scalarization of a cone metric to prove that the topology generated by any cone metric is equivalent to a topology generated by a related metric. We then analyze the case of an ordering cone with empty interior and we provide alternative definitions based on the notion of interior cone. Finally we discuss the implications of such cone metrics in the theory of iterated funct...

This chapter presents the application of a comprehensive statistical analysis for both algorithmic performance comparison and optimal parameter estimation on a multi-objective digital signal processing problem. The problem of designing optimum digital finite impulse response (FIR) filters with the simultaneous approximation of the filter magnitude and phase is posed as a multiobjective optimiza...

A continuous time mean variance (MV) problem optimizes the biobjective criteria (V , E), representing variance V and expected value E, respectively, of a random variable at the end of a time horizon T . This problem is computationally challenging since the dynamic programming principle cannot be directly applied to the variance criterion. An embedding technique has been proposed in [D. Li and W...