Every TVS-cone metric space is topologically isomorphic to a topological metric space. In this paper, by using a nonlinear scalarization, we give some fixed point results with nonlinear contractive conditions on TVS-cone metric spaces.

One task of all Fortran 90 compilers is to scalarize the array syntax statements of a program into equivalent sequential code. Most compilers require multiple passes over the program source to ensure correctness of this translation, since their analysis algorithms only work on the scalarized form. These same compilers then make additional subsequent passes to perform loop optimizations such as ...

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...

In decision-theoretic planning problems, such as (partially observable) Markov decision problems [Wiering and Van Otterlo, 2012] or coordination graphs [Guestrin et al., 2002], agents typically aim to optimize a scalar value function. However, in many real-world problems agents are faced with multiple possibly conflicting objectives, e.g., maximizing the economic benefits of timber harvesting w...

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...

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...

We study static and spherically symmetric charged stars with a nontrivial profile of the scalar field $\phi$ in Einstein-Maxwell-scalar theories. The is coupled to $U(1)$ gauge $A_{\mu}$ form $-\alpha(\phi)F_{\mu \nu}F^{\mu \nu}/4$, where $F_{\mu \nu}=\partial_{\mu}A_{\nu}-\partial_{\nu} A_{\mu}$ strength tensor. Analogous case black holes, we show that this type interaction can induce spontane...