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Vector continuous-time programming without differentiability

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第3期234卷 924-933页

作者： de Oliveira, Valeriano Antunes Univ Fed Uberlandia Fac Ciencias Integradas Pontal BR-38032000 Ituiutaba MG Brazil

In this work continuous-time programming problems of vector optimization are considered. Firstly, a nonconvex generalized Gordan's transposition theorem is obtained. Then, the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established. A scalar dual problem is introduced and duality theorems are given. No differentiability assumption is imposed. (C) 2010 Elsevier B.V. All rights reserved.

关键词： continuous-time programming Multiobjective programming Preinvex functions Scalarization Saddle point optimality Duality

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SADDLE-POINT TYPE OPTIMALITY CRITERIA, DUALITY AND A NEW APPROACH FOR SOLVING NONSMOOTH FRACTIONAL continuous-time programming PROBLEMS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第3期19卷 1931-1944页

作者： Jovic, Aleksandar Univ Belgrade Fac Math Dept Numer Math & Optimizat Studentski Trg 16 Belgrade 11000 Serbia

In this paper, fractional continuous-time programming problems with inequality phase constraints are considered. Optimality conditions and duality results under a certain regularity condition are derived. All functions are assumed to be nondifferentiable. These results improve and generalize a number of existing results in the area of fractional continuous-time program-ming. We provide a practical example to illustrate our results.

关键词： continuous-time programming fractional continuous-time programming saddle point optimality duality

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POST-OPTIMALITY SENSITIVITY ANALYSIS IN ABSTRACT SPACES WITH APPLICATIONS TO continuous-time programming-PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1985年第3期45卷 347-373页

作者： BUIE, RN ABRHAM, J UNIV TORONTO DEPT IND ENGNTORONTO M5S 1A1ONTARIOCANADA

The programming problem under consideration consists in maximizing a concave objective functional, subject to convex operator inequality contraints. The assumptions include the existence of an optimum solution, Fréchet differentiability of all operators involved, and the existence of the topological complement of the null space of the Fréchet derivative of the constraint operator. It is shown that the rate of change of the optimum value of the objective functional due to the perturbation is measured by the dual. The optimum values of the primal variables are locally approximated as linear functions of the perturbation; the theory of generalized inverse operators is used in the approximation. We give an approximation to the primal variables if the problem is perturbed. The results are specialized for some continuous-time and finite-dimensional cases. Two examples for finite-dimensional problems are given. We apply the theory to the continuous-time linear programming problem and prove some continuity results for the optimal primal and dual objective functionals.

关键词： Sensitivity analysis stability theory nonlinear problems continuous-time programming generalized inverse operators perturbed linearized constraints infinite-dimensional programs

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A Constant Rank Constraint Qualification in continuous-time Nonlinear programming

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SET-VALUED AND VARIATIONAL ANALYSIS 2021年第1期29卷 61-81页

作者： do Monte, Moises Rodrigues Cirilo de Oliveira, Valeriano Antunes UFU Inst Ciencias Exatas & Nat Pontal Campus Ituiutaba Ituiutaba MG Brazil Univ Estadual Paulista Unesp Inst Biociencias Letras & Ciencias Exatas Dept Matemat Aplicada Campus Sao Jose do Rio Preto BR-15054000 Sao Jose Do Rio Preto SP Brazil

The paper addresses continuous-time nonlinear programming problems with equality and inequality constraints. First and second order necessary optimality conditions are obtained under a constant rank type constraint qu... 详细信息

关键词： Nonlinear programming continuous-time programming Necessary optimality conditions Constraint qualifications Constant rank condition

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Optimality conditions and duality models for a class of nonsmooth continuous-time generalized fractional programming problems

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OPTIMIZATION 2002年第2期51卷 353-399页

作者： Zalmai, GJ No Michigan Univ Dept Math & Comp Sci Marquette MI 49855 USA

Both parametric and parameter-free station any-point-type and saddle-point-type necessary and sufficient optimality conditions are established for a class of nonsmooth continuous-time generalized fractional programming problems with Volterra-type integral inequality and nonnegativity constraints. These optimality criteria are then utilized for constructing ten parametric and parameter-free Wolfe-type and Lagrangian-type dual problems and for proving weak, strong, and strict converse duality theorems. Furthermore, it is briefly pointed out how similar optimality and duality results can be obtained for two important special cases of the main problem containing arbitrary norms and square roots of positive semidefinite quadratic forms, All the results developed here are also applicable to continuous-time programming problems with fractional, discrete max, and conventional objective functions, which are special cases of the main problem studied in this paper.

关键词： continuous-time programming generalized fractional objective functions subgradients caratheodory integrands optimality conditions dual problems duality theorems

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continuous-time generalized fractional programming

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Optimization 1996年第3期36卷 195-217页

作者： Zalmai, G.J. Dept. of Math. and Computer Science Northern Michigan University Marquette MI 49855 United States

Both parametric and parameter-free necessary and sufficient optimality conditions and several duality models are presented for a class of continuous-time generalized fractional programming problems. These results improve and extend a number of existing results in the area of continuous-time programming and, furthermore, provide continuous-time analogues of various cognate results previously established for certain categories of finite-dimensional generalized fractional, fractional, discrete minmax, and conventional nonlinear programming problems.

关键词： continuous-time programming Duality models Duality theorems Generalized fractional objective function Optimality conditions

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continuous-time multiobjective fractional programming

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Optimization 1996年第1期37卷 1-25页

作者： Zalmai, G.J. Dept. of Math. and Computer Science Northern Michigan University Marquette MI 49855 United States

Both parametric and semiparametric necessary and sufficient proper efficiency principles are established for a class of continuous-time multiobjective fractional programming problems. Based on the forms and contents of these proper efficiency results, two parametric and four semiparametric duality models are constructed and, in each case, weak and strong duality theorems are proved. These proper efficiency and duality results contain, as special cases, similar results for continuous-time programming problems with multiple nonfractional, single fractional, and conventional objective functions. These results improve and generalize a number of existing results in the area of continuous-time programming and, moreover, provide continuous-time analogues of various kindred results previously obtained for certain classes of finite-dimensional nonlinear programming problems.

关键词： continuous-time programming Dual problems Duality theorems Multiple fractional objective functions Proper efficiency conditions

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Optimality conditions and duality for a class of continuous-time linear optimization problems

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COMPUTATIONAL & APPLIED MATHEMATICS 2024年第5期43卷 1-29页

作者： de Oliveira, Valeriano Antunes Univ Estadual Paulista UNESP Inst Biociencias Letras & Ciencias Exatas Dept Matemat Rua Cristovao Colombo 2265 BR-15054000 Sao Jose Do Rio Preto SP Brazil

In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak and strong duality properties as well as the complementary slackness theorem are established. A result concerning the existence of solutions is also stated.

关键词： continuous-time programming Linear programming Optimality conditions Duality

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LINEAR-QUADRATIC programming AND OPTIMAL-CONTROL

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1987年第3期25卷 781-814页

作者： ROCKAFELLAR, RT Washington University Seattle

A generalized approach is taken to linear and quadratic programming in which dual as well as primal variables may be subjected to bounds, and constraints may be represented through penalties. Corresponding problem models in optimal control related to continuous-time programming are then set up and theorems on duality and the existence of solutions are derived. Optimality conditions are obtained in the form of a global saddle point property which decomposes into an instantaneous saddle point condition on the primal and dual control vectors at each time, along with an endpoint condition.

关键词： 49B10 90C20 90C05 Linear-quadratic programming dual control problems intertemporal programming continuous-time programming penalty representation of constraints

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Necessary conditions for continuous-time optimization under the Mangasarian-Fromovitz constraint qualification

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OPTIMIZATION 2020年第4期69卷 777-798页

作者： Cirilo do Monte, Moises Rodrigues de Oliveira, Valeriano Antunes Univ Estadual Paulista Unesp Inst Biociencias Letras & Ciencias Exatas Dept Matemat Aplicada Campus Sao Jose Rio Preto Sao Paulo Brazil Univ Fed Uberlandia UFU Inst Ciencias Exatas & Nat Pontal Campus Ituiutaba Uberlandia MG Brazil

In this paper, a Mangasarian-Fromovitz-type regularity condition is presented with the purpose of obtaining first order necessary optimality conditions for continuous-time nonlinear programming problems with both equality and inequality constraints. The Karush-Kuhn-Tucker-type optimality conditions are obtained by means of geometric ideas, where a theorem of the alternative and a uniform implicit function theorem are the main tools.

关键词： continuous-time programming necessary conditions constraint qualifications Mangasarian-Fromovitz conditions

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