A Lagrange multiplierrules that uses small generalized gradients is introduced. It includes both inequality and set constraints. The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus. Its convex hull is the generalized gradient of Michel and Penot if a function is Lipschitz. Th...

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 ...

The paper presents a general purpose software system for optimization and decision support, called Optima-Plus. It consists of two independent parts LIOP-1 system and MKO-2.1 system. Optima-Plus system is designed to support the decision maker (DM) in modeling and solving different problems of linear and linear integer single-criterion and multicriteria optimization. The system implements three...

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...

Abstract: It is of crucial importance to develop risk-averse models for multicriteria decision making under uncertainty. A major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints. These problems typically involve a univariate stochastic preference relation, often based on stochastic dominance or a coherent risk measure s...

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...

We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwell-scalar models flat spacetime, wherein scalar field $\phi$ is nonminimally coupled to Maxwell electrodynamics. This setup serves as toy model for (vacuum) black holes Einstein-Maxwell-scalar (generalized scalar-tensor) models. In case, unlike hole cases, closed-form solutions exist scalarized confi...

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...