\relax 
\@writefile{toc}{\contentsline {chapter}{\numberline {4.}Finite-Lifetime Optimization Results}{74}{chapter.4}}
\newlabel{ch:optimization_results}{{4}{74}{Finite-Lifetime Optimization Results\relax }{chapter.4}{}}
\@writefile{default}{\indexentry{solitary agent model!classical analysis!optimization|(hyperpage}{74}}
\@writefile{default}{\indexentry{solitary agent model!processing-only analysis!optimization|(hyperpage}{74}}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}Optimization of a Rational Objective Function}{74}{section.4.1}}
\newlabel{sec:optimization_rational}{{4.1}{74}{Optimization of a Rational Objective Function\relax }{section.4.1}{}}
\@writefile{default}{\indexentry{rational objective function|(hyperpage}{74}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.1}The Generalized Problem}{75}{subsection.4.1.1}}
\@writefile{toc}{\contentsline {subsubsection}{The Decision Variables and Constraints}{75}{section*.41}}
\citation{Bertsekas95}
\@writefile{toc}{\contentsline {subsubsection}{Generalized Advantage, Disadvantage, and Objective}{76}{section*.42}}
\@writefile{toc}{\contentsline {subsubsection}{Notation}{76}{section*.43}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.2}The Optimization Procedure}{76}{subsection.4.1.2}}
\newlabel{sec:optimization_procedure}{{4.1.2}{76}{The Optimization Procedure\relax }{subsection.4.1.2}{}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{77}}
\@writefile{brf}{\backcite{Bertsekas95}{{77}{4.1.2}{subsection.4.1.2}}}
\citationpage{Bertsekas95}{\hyperpage{77}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{77}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{77}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{77}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{77}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{77}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{78}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{78}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{78}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{78}}
\@writefile{toc}{\contentsline {subsubsection}{First-Order Necessary Conditions}{78}{section*.44}}
\newlabel{eq:JAD_star_notation}{{4.1}{78}{First-Order Necessary Conditions\relax }{equation.4.1.1}{}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{78}}
\newlabel{eq:first_order_gradient}{{4.2}{78}{First-Order Necessary Conditions\relax }{equation.4.1.2}{}}
\newlabel{eq:first_order_multipliers_pminus}{{4.3a}{79}{First-Order Necessary Conditions\relax }{equation.4.1.3a}{}}
\newlabel{eq:first_order_multipliers_pplus}{{4.3b}{79}{First-Order Necessary Conditions\relax }{equation.4.1.3b}{}}
\newlabel{eq:first_order_multipliers_tauminus}{{4.3c}{79}{First-Order Necessary Conditions\relax }{equation.4.1.3c}{}}
\newlabel{eq:first_order_multipliers_tauplus}{{4.3d}{79}{First-Order Necessary Conditions\relax }{equation.4.1.3d}{}}
\@writefile{toc}{\contentsline {paragraph}{Preference Probabilities:}{79}{section*.45}}
\newlabel{eq:pj_first_order_unconst}{{4.4a}{79}{Preference Probabilities:\relax }{Item.18}{}}
\newlabel{eq:pj_first_order_minconst}{{4.4b}{79}{Preference Probabilities:\relax }{Item.19}{}}
\newlabel{eq:pj_first_order_maxconst}{{4.4c}{79}{Preference Probabilities:\relax }{Item.20}{}}
\@writefile{toc}{\contentsline {paragraph}{Processing Times:}{80}{section*.46}}
\newlabel{eq:tauj_first_order_unconst}{{4.5a}{80}{Processing Times:\relax }{Item.21}{}}
\newlabel{eq:tauj_first_order_minconst}{{4.5b}{80}{Processing Times:\relax }{Item.22}{}}
\newlabel{eq:tauj_first_order_maxconst}{{4.5c}{80}{Processing Times:\relax }{Item.23}{}}
\@writefile{toc}{\contentsline {subsubsection}{Second-Order Necessary Conditions}{81}{section*.47}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{81}}
\newlabel{eq:second_order_hessian}{{4.6}{81}{Second-Order Necessary Conditions\relax }{equation.4.1.6}{}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{81}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{81}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{81}}
\@writefile{toc}{\contentsline {paragraph}{Elimination of Active Preference Probability Constraints:}{81}{section*.48}}
\@writefile{toc}{\contentsline {paragraph}{Elimination of Active Processing Time Constraints:}{81}{section*.49}}
\@writefile{toc}{\contentsline {paragraph}{Elimination of Off-Diagonal Terms:}{82}{section*.50}}
\newlabel{eq:second_derivative_J_pp_ptau}{{4.7}{82}{Elimination of Off-Diagonal Terms:\relax }{equation.4.1.7}{}}
\newlabel{eq:second_derivative_J_tautau}{{4.8}{82}{Elimination of Off-Diagonal Terms:\relax }{equation.4.1.8}{}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{82}}
\citation{SK86}
\@writefile{toc}{\contentsline {paragraph}{Impact of Inactive Preference Probability Diagonals:}{83}{section*.51}}
\aiexplicit{Ludwig Otto Hesse}{\hyperpage{83}}
\newlabel{eq:pj_second_order_necessary}{{4.9}{83}{Impact of Inactive Preference Probability Diagonals:\relax }{equation.4.1.9}{}}
\@writefile{toc}{\contentsline {paragraph}{Definiteness from Inactive Processing Time Diagonals:}{83}{section*.52}}
\newlabel{eq:tauj_second_order_necessary}{{4.10}{83}{Definiteness from Inactive Processing Time Diagonals:\relax }{equation.4.1.10}{}}
\@writefile{toc}{\contentsline {subsubsection}{Second-Order Sufficiency Conditions}{83}{section*.53}}
\aiexplicit{Joseph-Louis Lagrange}{\hyperpage{83}}
\@writefile{default}{\indexentry{extreme-preference rule (EPR)|(indexdef}{84}}
\@writefile{toc}{\contentsline {paragraph}{The Extreme-Preference Rule:}{84}{section*.54}}
\@writefile{acronyms}{\indexentry{EPR@[EPR] \index {extreme-preference rule (EPR)"|indexglo}extreme-preference rule~\bhypersym {acro:EPR}|nopage}{84}}
\newlabel{def:acro:EPR}{{4.1.2}{84}{The Extreme-Preference Rule:\relax }{section*.54}{}}
\@writefile{brf}{\backcite{SK86}{{84}{4.1.2}{section*.54}}}
\citationpage{SK86}{\hyperpage{84}}
\@writefile{default}{\indexentry{zero-one rule|indexdef}{84}}
\@writefile{default}{\indexentry{extreme-preference rule (EPR)|)indexdef}{84}}
\@writefile{default}{\indexentry{EPR|see{extreme-preference rule}}{84}}
\@writefile{toc}{\contentsline {paragraph}{Problems with Sufficiency at Zero Preference Probability:}{84}{section*.55}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1.3}Solutions to Special Cases}{84}{subsection.4.1.3}}
\@writefile{toc}{\contentsline {subsubsection}{Constant Disadvantage Case}{85}{section*.56}}
\@writefile{default}{\indexentry{rational objective function!optimal solution!constant disadvantage|(hyperpage}{85}}
\newlabel{item:constant_disadv_exclusion}{{i}{85}{Constant Disadvantage Case\relax }{Item.24}{}}
\newlabel{item:constant_disadv_differentiability}{{ii}{85}{Constant Disadvantage Case\relax }{Item.25}{}}
\newlabel{item:constant_disadv_same_sign}{{iii}{85}{Constant Disadvantage Case\relax }{Item.26}{}}
\newlabel{item:constant_disadv_nonzero_Dstar}{{iv}{85}{Constant Disadvantage Case\relax }{Item.27}{}}
\newlabel{item:constant_disadv}{{v}{85}{Constant Disadvantage Case\relax }{Item.28}{}}
\newlabel{item:constant_disadv_conv_left}{{vi.a}{85}{Constant Disadvantage Case\relax }{Item.30}{}}
\newlabel{item:constant_disadv_conv_right}{{vi.b}{85}{Constant Disadvantage Case\relax }{Item.31}{}}
\newlabel{item:constant_disadv_conv_middle}{{vi.c}{85}{Constant Disadvantage Case\relax }{Item.32}{}}
\newlabel{item:constant_disadv_convexity}{{vi}{85}{Constant Disadvantage Case\relax }{Item.32}{}}
\citation{SK86}
\@writefile{brf}{\backcite{SK86}{{86}{4.1.3}{Item.32}}}
\citationpage{SK86}{\hyperpage{86}}
\@writefile{default}{\indexentry{task-type choice                 problem|hyperpage}{86}}
\newlabel{eq:generalized_prey_ordering}{{4.11}{86}{Constant Disadvantage Case\relax }{equation.4.1.11}{}}
\citation{SK86}
\citation{Cha76}
\citation{Cha73}
\citation{SK86}
\@writefile{default}{\indexentry{rational objective function!optimal solution!constant disadvantage|)hyperpage}{87}}
\@writefile{toc}{\contentsline {subsubsection}{Decreasing Advantage-to-Disadvantage Ratio}{87}{section*.57}}
\@writefile{default}{\indexentry{rational objective function!optimal solution!decreasing advantage-to-disadvantage|(hyperpage}{87}}
\@writefile{default}{\indexentry{combined task-type and processing-length choice problem|hyperpage}{87}}
\@writefile{brf}{\backcite{SK86}{{87}{4.1.3}{section*.57}}}
\citationpage{SK86}{\hyperpage{87}}
\@writefile{default}{\indexentry{marginal value theorem (MVT)|hyperpage}{87}}
\@writefile{brf}{\backcite{Cha76}{{87}{4.1.3}{section*.57}}}
\@writefile{brf}{\backcite{Cha73}{{87}{4.1.3}{section*.57}}}
\citationpage{Cha76}{\hyperpage{87}}
\citationpage{Cha73}{\hyperpage{87}}
\@writefile{brf}{\backcite{SK86}{{87}{4.1.3}{section*.57}}}
\citationpage{SK86}{\hyperpage{87}}
\newlabel{item:decr_ratio_exclusion}{{i}{87}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.33}{}}
\newlabel{item:decr_ratio_differentiability}{{ii}{87}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.34}{}}
\newlabel{item:decr_ratio_same_sign}{{iii}{87}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.35}{}}
\newlabel{item:decr_ratio_nonzero_Dstar}{{iv}{87}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.36}{}}
\citation{SK86}
\newlabel{item:decr_ratio_same_sign_derivative}{{v}{88}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.37}{}}
\newlabel{item:decr_ratio}{{vi}{88}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.38}{}}
\newlabel{item:decr_ratio_second}{{vii}{88}{Decreasing Advantage-to-Disadvantage Ratio\relax }{Item.39}{}}
\newlabel{eq:generalized_prey_ordering_2}{{4.12}{88}{Decreasing Advantage-to-Disadvantage Ratio\relax }{equation.4.1.12}{}}
\@writefile{brf}{\backcite{SK86}{{88}{4.1.3}{equation.4.1.12}}}
\citationpage{SK86}{\hyperpage{88}}
\@writefile{default}{\indexentry{rational objective function!optimal solution!decreasing advantage-to-disadvantage|)hyperpage}{90}}
\@writefile{default}{\indexentry{rational objective function|)hyperpage}{90}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}Optimization of Specific Objective Functions}{90}{section.4.2}}
\newlabel{sec:optimization_specific}{{4.2}{90}{Optimization of Specific Objective Functions\relax }{section.4.2}{}}
\@writefile{default}{\indexentry{examples!analytical solutions|(indexdef}{90}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}Maximization of Rate of Excess Net Point Gain}{90}{subsection.4.2.1}}
\newlabel{sec:max_renpg}{{4.2.1}{90}{Maximization of Rate of Excess Net Point Gain\relax }{subsection.4.2.1}{}}
\@writefile{default}{\indexentry{examples!analytical solutions!rate of excess net gain|(indexdef}{90}}
\@writefile{default}{\indexentry{rate of excess net gain!analytical optimization|(hyperpage}{90}}
\citation{SK86}
\@writefile{default}{\indexentry{rate of excess net gain!analytical optimization|)hyperpage}{91}}
\@writefile{default}{\indexentry{examples!analytical solutions!rate of excess net gain|)indexdef}{91}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.2}Maximization of Discounted Net Gain}{91}{subsection.4.2.2}}
\@writefile{default}{\indexentry{examples!analytical solutions!discounted net gain|(indexdef}{91}}
\@writefile{brf}{\backcite{SK86}{{91}{4.2.2}{subsection.4.2.2}}}
\citationpage{SK86}{\hyperpage{91}}
\@writefile{default}{\indexentry{examples!analytical solutions!discounted net gain|)indexdef}{91}}
\citation{SK86}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.3}Maximization of Rate of Excess Efficiency}{92}{subsection.4.2.3}}
\@writefile{default}{\indexentry{examples!analytical solutions!excess efficiency|(indexdef}{92}}
\@writefile{brf}{\backcite{SK86}{{92}{4.2.3}{subsection.4.2.3}}}
\citationpage{SK86}{\hyperpage{92}}
\@writefile{default}{\indexentry{examples!analytical solutions!excess efficiency|)indexdef}{92}}
\@writefile{default}{\indexentry{examples!analytical solutions|)indexdef}{92}}
\@writefile{default}{\indexentry{solitary agent model!processing-only analysis!optimization|)hyperpage}{92}}
\@writefile{default}{\indexentry{solitary agent model!classical analysis!optimization|)hyperpage}{92}}
\@setckpt{oft_ch4_optimization_results}{
\setcounter{page}{93}
\setcounter{equation}{12}
\setcounter{enumi}{7}
\setcounter{enumii}{3}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{7}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{4}
\setcounter{section}{2}
\setcounter{subsection}{3}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{0}
\setcounter{table}{0}
\setcounter{disspage}{0}
\setcounter{NAT@ctr}{0}
\setcounter{parentequation}{5}
\setcounter{KVtest}{1}
\setcounter{subfigure}{0}
\setcounter{subfigure@save}{3}
\setcounter{lofdepth}{1}
\setcounter{subtable}{0}
\setcounter{subtable@save}{0}
\setcounter{lotdepth}{1}
\setcounter{Item}{39}
\setcounter{Hfootnote}{59}
\setcounter{section@level}{2}
}